Advertisements
Advertisements
Question
A gas is enclosed in a cylindrical can fitted with a piston. The walls of the can and the piston are adiabatic. The initial pressure, volume and temperature of the gas are 100 kPa, 400 cm3 and 300 K, respectively. The ratio of the specific heat capacities of the gas, Cp / Cv = 1.5. Find the pressure and the temperature of the gas if it is (a) suddenly compressed (b) slowly compressed to 100 cm3.
Advertisements
Solution
Initial pressure of the gas, P1 = 100 kPa
Initial volume of the gas,V1 = 400 cm3 = 400 × 10−6 m3
Initial temperature of the gas, T1 = 300 K
`gamma =("C"_"p")/("C"_"v") =1.5`
(a) The gas is suddenly compressed to volume, V2 = 100 cm3 .
So, this is an adiabatic process.
For an adiabatic process,
P1V1γ = P2V2γ
⇒ 105 × (400)1.5 = P2 (100)1.5
⇒ P2 =105 (4)1.5 = 800 kPa
Also,
T1Vγ−1 = T2V2γ−1
⇒ 300 × (400)1.5−1 = T2 (100)1.5−1
⇒ 300 × (400)0.5 = T2 (100)0.5
⇒ T2 = 600 K
(b) If the container is slowly compressed, the heat transfer is zero, even thought the walls are adiabatic.
Thus, the values remain same. Thus,
P2 = 800 kPa
T2 = 600 K
APPEARS IN
RELATED QUESTIONS
A gas is kept in a rigid cubical container. If a load of 10 kg is put on the top of the container, does the pressure increase?
If it were possible for a gas in a container to reach the temperature 0 K, its pressure would be zero. Would the molecules not collide with the walls? Would they not transfer momentum to the walls?
Explain why cooking is faster in a pressure cooker.
A gas behaves more closely as an ideal gas at
In an adiabatic process on a gas with γ = 1.4, the pressure is increased by 0.5%. The volume decreases by about
A vessel of volume V0 contains an ideal gas at pressure p0 and temperature T. Gas is continuously pumped out of this vessel at a constant volume-rate dV/dt = 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 time, (b) the time taken before half the original gas is pumped out.
Use R = 8.3 J K−1 mol−1
The initial pressure and volume of a given mass of a gas (Cp/Cv = γ) are p0 and V0. The gas can exchange heat with the surrounding. (a) It is slowly compressed to a volume V0/2 and then suddenly compressed to V0/4. Find the final pressure. (b) If the gas is suddenly compressed from the volume V0 to V0/2 and then slowly compressed to V0/4, what will be the final pressure?
Two glass bulbs of equal volume are connected by a narrow tube and are filled with a gas at 0°C at a pressure of 76 cm of mercury. One of the bulbs is then placed in melting ice and the other is placed in a water bath maintained at 62°C. What is the new value of the pressure inside the bulbs? The volume of the connecting tube is negligible.
On a winter day, the outside temperature is 0°C and relative humidity 40%. The air from outside comes into a room and is heated to 20°C. What is the relative humidity in the room? The saturation vapour pressure at 0°C is 4.6 mm of mercury and at 20°C it is 18 mm of mercury.
The temperature and humidity of air are 27°C and 50% on a particular day. Calculate the amount of vapour that should be added to 1 cubic metre of air to saturate it. The saturation vapour pressure at 27°C = 3600 Pa.
Use R = 8.3 J K-1 mol-1
The temperature and relative humidity in a room are 300 K and 20% respectively. The volume of the room is 50 m3. The saturation vapour pressure at 300 K 3.3 kPa. Calculate the mass of the water vapour present in the room.
Use R = 8.3 J K-1 mol-1
A bucket full of water is placed in a room at 15°C with initial relative humidity 40%. The volume of the room is 50 m3. (a) How much water will evaporate? (b) If the room temperature is increased by 5°C, how much more water will evaporate? The saturation vapour pressure of water at 15°C and 20°C are 1.6 kPa and 2.4 kPa respectively.
Use R = 8.3 J K-1 mol-1
A cuboidal container having dimensions 2 m × 1.5 m × 0.5 m holds a mixture of 12 g of He, 36 g of Ar, and 20 g of Ne, If the container is maintained at 300 K, Find the pressure exerted by the mixture (given MHe = 4, MAr = 40, MNe = 20).
If 1022 gas molecules each of mass 10-26 kg collide with a surface (perpendicular to it) elastically per second over an area of 1 m2 with a speed of 104 m/s, the pressure exerted by the gas molecules will be of the order of ______.
In a cubical box of volume V, there are N molecules of a gas moving randomly. If m is mass of each molecule and v2 is the mean square of x component of the velocity of molecules, then the pressure of the gas is ______.
Air separated from the atmosphere by a column of mercury of length h = 15 cm is present in a narrow cylindrical two-soldered at one end. When the tube is placed horizontally the air occupies a volume V1 = 240 mm3. When it is set vertically with its open end upwards the volume of the air is V2 = 200 mm3. The atmospheric pressure during the experiment is 7n cm of Hg where n is a single digit number. n will be ______.
