Question

A diatomic gas does 200 j of work when it expands isobarically. Find the heat given to the gas in the process

Answer 1

1. Question⇒  A diatomic gas does 200 j of work when it expands isobarically. Find the heat given to the gas in the process.

Explanation:

• Given
• Work done by Isobaric ( constant pressure )
• Process - W 200J
• W = P ∆ V = 200 J from ideal gas equation at constable speed we have
• P∆V = nR∆T = ∆T P∆VnR= 80 JnR------- 1
• Also Change in internal energy during the process is given by∆U. =nCv∆T=nRγ-1∆TFor diaomic gas, γ=7/5
• Putting the value of ∆T from Eq.1 we get∆U=nR75-180 JnR=52×200 J=200 J 
• From 1st law of thermodynamicsHeat given to gas is given by∆Q=∆U+W⇒∆Q=200 J+200 J=480 J   Answer

Answer 2

Solution :

For an diatomic gas

$\sf \implies C_v = \frac{5}{2} \\ \\ \sf \implies C_p = \frac{7}{2}$

The work done in an isobaric process is

$\sf \implies W = p(V_2 -V_1) \\ \\\sf \implies W = nRT_2 - nRT_1 \\ \\\sf \implies T_2 - T_1 = \frac{W}{nR}$

The heat given in an isobaric process is

$\sf \implies Q = nC_p(T_2 - T_1) \\ \\\sf \implies Q = nC_p \frac{W}{nR} = \frac{7}{2}W \\ \\\sf \implies Q = \frac{7}{2} \times 200 \\ \\\sf \implies Q = 700\:J$