5000J of heat are added to two moles an ideal monoatomic gas, initially at a temperature of 500K, while the gas performs 7500J of work. What is the final temperature of the gas ? (in Kelvin)
ΔU = ΔQ – ΔW = 5000  7500
ΔU = –2500 J
⇒ ΔT = –100 K
⇒ T = 500  100 = 400 K
The correct answer is: 400
For a diatomic ideal gas near room temperature, what fraction of heat supplied is available for external work if gas is expanded at constant pressure
In the process of expansion at constant pressure p, assuming that the volume increases from V_{1} to V_{2} and temperature change from T_{1} to T_{2} , we have
pV_{1} = nRT_{1}
pV_{2} = nRT_{2}
In this process, the work done by the system on the outside world is W = p(V_{2} V_{1} )= nRΔT and increase in internal energy of the system is
ΔU = C_{v}ΔT
∴
The correct answer is: 0.286
A gas has pressure p and volume V. It is now compressed adiabatically to 1/32 times the original volume. If (32)^{1.4} = 128, the final pressure in terms of p is
For an adiabatic process,
⇒
⇒ p = (32)^{1.4} p
⇒ p_{1} = 128p.
The correct answer is: 128
1cm^{3} of water at its boiling point absorbs 540 calories of heat to become steam with a volume of 1671 cm^{3}. If the atmospheric pressure is 1.013 × 10^{5} N/m^{2} and mechanical equivalent of heat = 4.19 J/calorie, the energy spent in this process in overcoming intermolecular forces is (in calories)
Energy spent in overcoming intermolecular forces
ΔU = ΔQ – ΔW
= ΔQ – p(V_{2} – V_{1})
= 500cal.
The correct answer is: 500
An ideal gas at 27ºC is compressed adiabatically to 8/27 of its original volume. If then the rise in temperature (in Kelvin) is
For adiabatic process = constant
⇒
T_{2} = 675K
ΔT = 675–300
= 375K
The correct answer is: 375
Two systems with heat capacities 100cal/gmK and 200cal/gmK interact thermally and come to a common temperature 400K. If the initial temperature of system 1 is 500K, what was the initial temperature of systems (in Kelvin) scale
Let initial temperature of system 2 is T_{2}. According to conservation of energy, we know that heat released from one system is equal to the heat absorbed by the other system, i.e.
C_{1} (T_{f} – T_{1} ) = C_{2} (T_{2} –T_{f} )
= –50+400
T_{2} = 350K
The correct answer is: 350
During an adiabatic processes, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio Cp /C_{V} for the gas is
But for an adiabatic processes,
⇒
⇒
The correct answer is: 1.5
When an ideal gas is heated under constant pressure, then what percentage of given heat energy will be utilized in doing external work?
∴ Percentage energy utilized in doing external work =
The correct answer is: 40
5 mole of hydrogen gas is heated from 30ºC to 60ºC at constant pressure. Heat given to the gas is in calories (given R = 2cal/moleºC)
= 1050 calories
The correct answer is: 1050
Three liquids with masses m_{1}, m_{2}, m_{3} are thoroughly mixed. If their specific heats are C_{1}, C_{2} and C_{3} and their temperature T_{1}, T_{2}, T_{3}, then the temperature of the mixture is given that
Let the final temperature be T K. Total heat supplied by 3 liquids in coming down to
Total heat used by three liquids in raising temperature from 0º to TºC
from (1) & (2),
⇒
T = 558.8K
The correct answer is: 558.8
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