At pressure P and absolute temperature T, a mass M of an ideal gas fills a closed container of volume V. An additional mass 2 M of the same gas is added into the container and the volume is then reduced to (V/3) and the temperature to (T/3). If now the pressure of the gas is n P, then find n.

Question

At pressure P and absolute temperature T, a mass M of an ideal gas fills a closed container of volume V. An additional mass 2 M of the same gas is added into the container and the volume is then reduced to (V/3) and the temperature to (T/3). If now the pressure of the gas is n P, then find n. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

If M0 is the molecular mass of the gas, then for initial condition P V=(M/M0) . R T ...(i) After 2 M mass has been added, P' ⋅ (V/3)=(3 M/M0) ⋅ R ⋅ (T/3) ...(ii) Dividing (ii) by (i), we get P'=3 P'

Q. At pressure P and absolute temperature T, a mass M of an ideal gas fills a closed container of volume V. An additional mass 2M of the same gas is added into the container and the volume is then reduced to 3V​ and the temperature to 3T​. If now the pressure of the gas is nP, then find n.

If M0​ is the molecular mass of the gas, then for initial condition PV=M0​M​.RT...(i) After 2M mass has been added, P′⋅3V​=M0​3M​⋅R⋅3T​...(ii) Dividing (ii) by (i), we get P′=3P′

If $M_{0}$ is the molecular mass of the gas, then for initial condition
$P V = \frac{M}{M _{0}} . RT ... (i)$
After $2 M$ mass has been added,
$P^{'} \cdot \frac{V}{3} = \frac{3 M}{M _{0}} \cdot R \cdot \frac{T}{3} ... (ii)$
Dividing (ii) by (i), we get
$P^{'} = 3 P^{'}$