Use R=8.3 J/mol-K wherever required. On a winter day, the outside temperature is 0°C
Question: Use $R=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. On a winter day, the outside temperature is $0^{\circ} \mathrm{C}$ and relative humidity $40 \%$. The air from outside comes into a room and is heated to $20^{\circ} \mathrm{C}$. What is the relative humidity in the room? The saturation vapour pressure at $0^{\circ} \mathrm{C}$ is $4.6 \mathrm{~mm}$ of mercury and at $20^{\circ} \mathrm{C}$ it is $18 \mathrm{~mm}$ of mercury. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. A faulty barometer contains certain amount of air and
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. A faulty barometer contains certain amount of air and saturated water vapour. It reads $74.0 \mathrm{~cm}$ when the atmospheric pressure is $76.0 \mathrm{~cm}$ of mercury and reads $72.10 \mathrm{~cm}$ when the atmospheric pressure is $74.0 \mathrm{~cm}$ of mercury. Saturation vapour pressure at the air temperature $=1.0 \mathrm{~cm}$ of mercury. Find the length of the barometer tube above the mercury level i...
Read More →Use R=8.3 J/mol-K wherever required. 50 cc of oxygen is collected in an inverted gas jar over water.
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. $50 \mathrm{cc}$ of oxygen is collected in an inverted gas jar over water. The atmospheric pressure is $99.4 \mathrm{kPa}$ and the room temperature is $27^{\circ} \mathrm{C}$. The water level in the jar is same as the level outside. The saturation vapour pressure at $27^{\circ} \mathrm{C}$ is $3.4 \mathrm{kPa}$. Calculate the number of moles of oxygen collected in the jar. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. A barometer correctly reads the atmospheric
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. A barometer correctly reads the atmospheric pressure as $76 \mathrm{~cm}$ of mercury. Water droplets are slowly introduced into the barometer tube by a dropper. The height of the mercury column first decreases and then becomes constant. If the saturation vapour pressure at atmospheric temperature is $0.80 \mathrm{~cm}$ of mercury, find the height of the mercury column when it reaches its minimum value. Soluti...
Read More →Use R=8.3 J/mol-K wherever required.
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. $50 \mathrm{~m}^{3}$ of saturated vapour is cooled down from $30^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{C}$. Find the mass of the water condensed. The absolute humidity of saturated water vapour is $30 \mathrm{~g} / \mathrm{m}^{3}$ at $30^{\circ} \mathrm{C}$ and $16 \mathrm{~g} / \mathrm{m}^{3}$ at $20^{\circ} \mathrm{C}$. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. A glass contains some water at room temperature 20°C .
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. A glass contains some water at room temperature $20^{\circ} \mathrm{C}$. Refrigerated water is added to it slowly. When the temperature of the glass reaches $10^{\circ} \mathrm{C}$, small droplets condense on the outer surface. Calculate the humidity in the room. The boiling point of water at a pressure of $17.5 \mathrm{~mm}$ of mercury is $20^{\circ} \mathrm{C}$ and at $8.9$ $\mathrm{mm}$ of mercury it is $1...
Read More →Use R=8.3 J/mol-K wherever required. The human body has an average temperature of 98℉.
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. The human body has an average temperature of $98^{\circ} \mathrm{F}$. Assume that vapour pressure of the blood in the veins behaves like that of pure water. Find the minimum atmospheric pressure which is necessary to prevent the blood from boiling. Use figure of the text for the vapour pressures. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. Using figure of the text,
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Using figure of the text, find the boiling point of methyl alcohol at $1 \mathrm{~atm}(760 \mathrm{~mm}$ of mercury) and at $0.5$ atm. Solution: At pressure of $760 \mathrm{~mm}$ we drop perpendicular on temperature axis, So, $\mathrm{T}=65^{\circ} \mathrm{C}$ Similarly, at $0.5$ atm, $T=48^{\circ} \mathrm{C}$...
Read More →Use R=8.3 J/mol-K wherever required. A barometer tube is 80 cm long (above mercury reservoir).
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. A barometer tube is $80 \mathrm{~cm}$ long (above mercury reservoir). It reads $76 \mathrm{~cm}$ on a particular day. A small amount of water is introduced in the tube and the reading drops to $75.4 \mathrm{~cm}$. Find the relative humidity in the space above the mercury column if the saturation vapor pressure at the room temperature is $1.0 \mathrm{~cm}$. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. Pure water vapor is trapped in a vessel of
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Pure water vapor is trapped in a vessel of volume $10^{\mathrm{cm}^{3}}$. The relative humidity is $40 \%$. The vapour is compressed slowly and isothermally. Find the volume of vapour at which it will start condensing. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. The temperature and the dew point in an open room
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. The temperature and the dew point in an open room are $20^{\circ} \mathrm{C}$ and $10^{\circ} \mathrm{C}$. If the room temperature drops to $15^{\circ} \mathrm{C}$, what will be the new dew point? Solution: Air becomes saturated at $10^{\circ} \mathrm{C}$. If room temperature falls to $15^{\circ} \mathrm{C}$ then also dew point $=10^{\circ} \mathrm{C}$....
Read More →Use R=8.3 J/mol-K wherever required. The condition of air in a closed room is described as follows.
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. The condition of air in a closed room is described as follows. Temperature $=25^{\circ} \mathrm{C}$, relative humidity $=60 \%$, pressure=104 $\mathrm{kPa}$. If all the water vapour is removed from the room without changing the temperature, what will be the new pressure? The saturation vapour pressure at $25^{\circ} \mathrm{C}=3.2 \mathrm{kPa}$. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. The weather report reads,
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. The weather report reads, "Temperature $20{ }^{\circ} \mathrm{C}$ : Relative humidity $100 \% "$. What is the dew point? Solution:...
Read More →Use R=8.3 J/mol-K wherever required. Two glass bulbs of equal volume are connected
Question: Use $R=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Two glass bulbs of equal volume are connected by a narrow tube and are filled with a gas at $0^{\circ} \mathrm{C}$ at a pressure of $76 \mathrm{~cm}$ of mercury. One of the bulbs is then placed in a water bath maintained at $62^{\circ} \mathrm{C} .$ What is the new value of the pressure inside the bulbs? The volume of the connecting tube is negligible. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. An ideal gas is kept in a long cylindrical vessel
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. An ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional area 10 $\mathrm{cm}^{2}$ and weight $1 \mathrm{~kg}$. The length of the gas column in the vessel is $20 \mathrm{~cm}$. The atmospheric pressure is $100 \mathrm{kPa}$. The vessel is now taken into a spaceship revolving round the earth as a satellite. The air pressure in the spaceship is maintained at $100 \m...
Read More →Use R=8.3 J/mol-K wherever required. An ideal gas is kept in a long cylindrical vessel fitted
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. An ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional area 10 $\mathrm{cm}^{2}$ and weight $1 \mathrm{~kg}$. The vessel itself is kept in a big chamber containing air at atmospheric pressure $100 \mathrm{kPa}$. The length of the gas column is $20 \mathrm{~cm}$. If the chamber is now completely evacuated by an exhaust pump, what will be the length of the gas col...
Read More →Use R=8.3 J/mol-K wherever required. Figure shows a large closed cylindrical tank containing water.
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Figure shows a large closed cylindrical tank containing water. Initially the air trapped above the water surface has a height ${ }^{h_{0}}$ and pressure ${ }_{2} p_{0}$ where $p_{0}$ is the atmospheric pressure. There is a hole in the wall of the tank at a depth $h_{1}$ below the top from which water comes out. A long vertical tube is connected as shown. (a) Find the height $h_{2}$ of the water in the long tu...
Read More →Use R=8.3 J/mol-K wherever required. Figure shows a cylindrical tube of cross-sectional
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Figure shows a cylindrical tube of cross-sectional area A fitted with two frictionless pistons. The pistons are connected to each other by a metallic wire. Initially, the temperature of the gas is $T_{0}$ and its pressure is $p_{0}$ which equals the atmospheric pressure. (a) What is the tension in the wire? (b) What will be the tension if the temperature is increased to $2^{T_{0}}$ ? Solution:...
Read More →Use R=8.3 J/mol-K wherever required. Figure shows a cylindrical tube of radius 5 cm
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Figure shows a cylindrical tube of radius $5 \mathrm{~cm}$ and length $20 \mathrm{~cm}$. It is closed by a tight-fitting cork. The friction co-efficient between the cork and the tube is $0.20$. The tube contains an ideal gas at a pressure of $1 \mathrm{~atm}$ and a temperature of $300 \mathrm{~K}$. The tube is slowly heated and it is found that the cork pops out when the temperature reaches $600 \mathrm{~K}$....
Read More →Use R=8.3 J/mol-K wherever required. Show that the internal energy of the air (treated as an ideal gas)
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Show that the internal energy of the air (treated as an ideal gas) contained in a room remains constant as the temperature changes between day and night. Assume that the atmospheric pressure around remains constant and the air in the room maintains this pressure by communicating with the surrounding through the windows etc. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. One mole of an ideal gas undergoes a process
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. One mole of an ideal gas undergoes a process $p=\frac{p_{0}}{1+\left(V / V_{0}\right)^{2}}$ Where ${ }^{p_{0}}$ and $V_{0}$ are constants. Find the temperature of gas when $V=V_{0}$. Solution:...
Read More →Use R=8.3 J/mol-K wherever required. A vessel of volume Vo contains an ideal
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. A vessel of volume $V_{0}$ contains an ideal gas at pressure $p_{0}$ and temperature $T$. Gas is continuously pumped out of this vessel at a constant-rate $\mathrm{dv} / \mathrm{dt}=\mathrm{r}$ keeping the temperature constant. The pressure of the gas being taken out equals the pressure inside the vessel. Find (a) the pressure of the gas as a function of gas, (b) the time taken before half the original gas is...
Read More →Use R=8.3 J/mol-K wherever required. Figure shows a cylindrical tube of length 30cm
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. Figure shows a cylindrical tube of length $30 \mathrm{~cm}$ which is partitioned by a tight-fitting separator. The separator is very weakly conducting and can freely slide along the tube. Ideal gases are filled in the two parts of the vessel. In the beginning, the temperatures in the parts A and B are $400 \mathrm{~K}$ and $100 \mathrm{~K}$ respectively. The separator slides to a momentary equilibrium positio...
Read More →Use R=8.3 J/mol-K wherever required. An ideal gas is trapped between a mercury column
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. An ideal gas is trapped between a mercury column and the closed end of a narrow vertical tube of uniform base containing the column. The upper end of the tube is open to the atmosphere. The atmospheric pressure equals $76 \mathrm{~cm}$ of mercury. The lengths of the mercury column and the trapped air column are $20 \mathrm{~cm}$ and $43 \mathrm{~cm}$ respectively. What will be the length of the air column whe...
Read More →Use R=8.3 J/mol-K wherever required. A glass tube, sealed at both ends, is 100 cm long.
Question: Use $\mathrm{R}=8.3 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ wherever required. A glass tube, sealed at both ends, is $100 \mathrm{~cm}$ long. It lies horizontally with the middle $10 \mathrm{~cm}$ containing mercury. The two ends of the tube contain air at $27^{\circ} \mathrm{C}$ and at a pressure $76 \mathrm{~cm}$ of mercury. The air column on one side is maintained at $0^{\circ} \mathrm{C}$ and the other side is maintained at $127^{\circ} \mathrm{C} .$ Calculated the length of the air...
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