In a thermodynamic process two moles of a monatomic ideal gas obeys P propto V-2. If temperature of the gas increases from 300 K to 400 K, then find work done by the gas (where R= universal gas constant).

Question

In a thermodynamic process two moles of a monatomic ideal gas obeys P propto V-2. If temperature of the gas increases from 300 K to 400 K, then find work done by the gas (where R= universal gas constant). (A) 200 R (B) -200 R (C) -100 R (D) -400 R

Tardigrade Admin · Accepted Answer

P propto V-2 P V2= constant Compare with P VN= constant then N=2 W=μ((R/1-N)) Δ T W=(μ R/1-N)(T2-T1) =(2 × R(400-300)/(1-2)) =-200 R

Q. In a thermodynamic process two moles of a monatomic ideal gas obeys $P \propto V^{- 2}$ . If temperature of the gas increases from $300 K$ to $400 K$ , then find work done by the gas (where $R =$ universal gas constant).

200 R

-200 R

-100 R

-400 R

$P \propto V^{- 2}$
$P V^{2} =$ constant
Compare with $P V^{N} =$ constant then $N = 2$
$W = μ (\frac{R}{1 - N}) Δ T$
$W = \frac{μ R}{1 - N} (T_{2} - T_{1})$
$= \frac{2 \times R ( 400 - 300 )}{( 1 - 2 )}$
$= - 200 R$

Q. In a thermodynamic process two moles of a monatomic ideal gas obeys P∝V−2. If temperature of the gas increases from 300K to 400K, then find work done by the gas (where R= universal gas constant).