Question

Three moles of hydrogen gas are compressed isothermally and reversibly from 60 L to 20 L and 8.50 kJ of work is done on it. Assuming ideal gas behavior, calculate the temperature of the gas.
A. 993 K
B. 1258 K
C. 1071 K
D. None of these

Answer 1

When a gas is compressed isothermally and reversibly then work will be done on the gas and when gas is expanded the work will be done by the gas. During the isothermal process the temperature of the system remains constant.

Complete solution:
When some process is done by the system or on the system at a constant temperature it is called an isothermal process. Reversible means that the process is done infinitely slowly so that the reverse from the final state exactly regenerates the initial state.
In this question we are given :
Number of moles of hydrogen gas, $n = 3$
Initial volume of gas, ${V_i} = 60{\text{ L}}$
Final volume of gas, ${V_f} = 20{\text{ L}}$
Work done on the gas, $W = 8.50{\text{ kJ}} \Rightarrow {\text{8500 J}}$
Work done by the gas in isothermal reversible process can be evaluated by using the relation given by
$W = - nRT\ln \dfrac{{{V_f}}}{{{V_i}}}$
On substituting the values we get
$8500 = - 3 \times 8.3145 \times T \times \ln \dfrac{{20}}{{60}}$
On simplifying we get
$T = \dfrac{{8500}}{{3 \times 8.3145 \times 1.098}}$
$T = 310.3{\text{ }}K$
So, the temperature of gas is 310 K

Hence the correct option is (D).

Note: Isothermal process is of two types :
1. Reversible isothermal process
2. Irreversible isothermal process
Reversible process proceeds extremely slowly while an irreversible process proceeds rapidly.In isothermal process internal energy remains constant expansion occurs with the absorption of heat while compression occurs with the evolution of heat.