$2$ moles of an ideal monatomic gas is heated through a process $T^{2} P^{3} =$ constant. If increase in temperature of gas is 100°C and work done by gas in this process is $(\frac{1000 R}{N})$ , find the value of $N$ . $(R$ is universal gas constant)

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Solution

$T^{2} P^{3} = C$
$(\frac{P V}{n R}) P^{3} = Z C \Rightarrow P^{5} V^{2} = C$
$\Rightarrow p V^{2 / 5} = C^{'}$
$C_{p r} = \frac{3 R}{2} \frac{R}{(\frac{2}{5} 1)} = (\frac{19 R}{6})$
$Q = n C_{p r} Δ T \Rightarrow Q = (2) (\frac{19 R}{6}) 100$
$Q = (\frac{1900 R}{3}), Δ u = (2) \times (\frac{3 R}{2}) \times 100$
$Δ u = 300 R$
$W = Q - Δ u = \frac{1900}{3} - 300 R = (\frac{1000 R}{3})$

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2 moles of an ideal monatomic gas is heated through a process T2P3= constant. If increase in temperature of gas is 100°C and work done by gas in this process is (1000RN), find the value of N. (R is universal gas constant)

T2P3=C (PVnR)P3=ZC⇒P5V2=C ⇒pV2/5=C′ Cpr=3R2R(251)=(19R6) Q=nCprΔT⇒Q=(2)(19R6)100 Q=(1900R3),Δu=(2)×(3R2)×100 Δu=300R W=Q−Δu=19003−300R=(1000R3)

$2$ moles of an ideal monatomic gas is heated through a process $T^{2} P^{3} =$ constant. If increase in temperature of gas is 100°C and work done by gas in this process is $(\frac{1000 R}{N})$ , find the value of $N$ . $(R$ is universal gas constant)