Question

An ideal diatomic gas occupies a volume V₁ at a pressure P₁. The gas undergoes a process in which the pressure is proportional to the volume. At the end of process the rms speed of the gas molecules has doubled from its initial value then the heat supplied to the gas in the given process is –

• A. 7 P₁V₁
• B. 8 P₁V₁
• C. 9 P₁V₁
• D. 10 P₁V₁

Answer 1

Answer: (C)

9 P₁V₁

Answer 2

As P ต V

\PV^–1= constant

Also, C = C_V – $\frac { \mathrm { R } } { \mathrm { x } - 1 }$ = $\frac { \mathrm { R } } { - 1 - 1 }$= 3R

But as rms speed is doubled therefore temperature becomes four times.

Hence, Q = nCDT = n ื 3R ื 3T_i = 9 nRT_i

= 9 P₁V₁