Question

Three moles of an ideal gas are compressed from 5.5 × 102

to 2.5 × 102 m3

. During the compression, 6.1 × 103

J of work is done on the gas, and heat is removed to keep the temperature of the gas constant at all times. 

Calculate the temperature of the gas.

Answer 1

Answer

Given :  Work of compression   $W_{com​}$ =$-6.1 × 10^3 \ J$

        Initial volume   V1​=0.55 L

        Final volume    V2​=0.25 L

Let the temperature of the gas be T 

As the temperature is constant all the time, thus the gas is compressed isothermally.

Workdone in isothermal compression      $W_{com}$ =$nRTln({V_2 \over V_1}​)$

∴    $-6.1 × 10^3 \ J=1\times 8.31 \times T ln({0.25\over5.5})$

= $-6.1 × 10^3 \ J=1\times 8.31 \times T(-ln{2})$

              (ln2=0.693)

⟹T=1059.2K