CP for an ideal gas is 5R/2. Two moles of this gas is taken in a rigid thermodynamic system and 600J heat is supplied to the gas. Calculate the increase in temperature (in Kelvin).

Question

CP for an ideal gas is 5R/2. Two moles of this gas is taken in a rigid thermodynamic system and 600J heat is supplied to the gas. Calculate the increase in temperature (in Kelvin). (A) 50/R (B) 100/R (C) 150/R (D) 200/R

Tardigrade Admin · Accepted Answer

From first Law of thermodynamics, Δ Q=W+Δ U ⇒ Δ Q=Δ U=nCVΔ T ⇒ Δ T=(Δ Q/n CV)=(Δ Q/n (CP - R)) =(600/2 × (3)2 R)=(200/R)K

Q. $C_{P}$ for an ideal gas is $5 R /2.$ Two moles of this gas is taken in a rigid thermodynamic system and $600 J$ heat is supplied to the gas. Calculate the increase in temperature (in Kelvin).

$50/ R$

$100/ R$

$150/ R$

$200/ R$

From first Law of thermodynamics,
$Δ Q = W + Δ U$
$\Rightarrow Δ Q = Δ U = n C_{V} Δ T$
$\Rightarrow Δ T = \frac{Δ Q}{n C _{V}} = \frac{Δ Q}{n ( C _{P} - R )}$
$= \frac{600}{2 \times \frac{3}{2} R} = \frac{200}{R} K$

Q. CP​ for an ideal gas is 5R/2. Two moles of this gas is taken in a rigid thermodynamic system and 600J heat is supplied to the gas. Calculate the increase in temperature (in Kelvin).

50/R

100/R

150/R

200/R