Question

A diatomic gas (γ = 1.4) does 500 J of work when it is expanded isobarically. Find the heat given to the gas in the process

1. 500 J
2. 250 J
3. 1750 J
4. 1000 J

Answer 1

Correct Answer - Option 3 : 1750 J

For a diatomic gas, C_V = 5R/2 and C_P = 7R/2.

For an isobaric process, work done is calculated as \(W\; = \;p\left( {{V_2} - {V_1}} \right)\; = \;nR\left( {{T_2} - {T_1}} \right)\)

\(\Rightarrow {T_2} - {T_1}\; = \;\frac{W}{{nR}}\;\)

The heat given in an isobaric process

\(Q\; = \;n{C_p}\left( {{T_2} - {T_1}} \right)\; = \;\frac{{n{C_p}W}}{{nR}}\; = \;\frac{{7RW}}{{2R}}\; = \;\frac{7}{2} \times W\; = \;\frac{7}{2} \times 500\; = \;1750\;J\)