One mole of an ideal gas at temperature T1 expands according to the law (.P/V.) = constant. Find the work done when the final temperature becomes T2 .

Question

One mole of an ideal gas at temperature T1 expands according to the law (.P/V.) = constant. Find the work done when the final temperature becomes T2 . (A) R(.T2-T1.) (B) (R/2)(.T2-T1.) (C) (R/4)(.T2-T1.) (D) PV(.T2-T1.)

Tardigrade Admin · Accepted Answer

W= displaystyle ∫ V1V2PdV= displaystyle ∫ textV1 textV2KVdV (∵ ( textitp/ textitV) = textitK = textconstant) ∴ textitW=(1/2) textitk( textitV22 - textitV12) PV=RT But P=RT ∴ textitKV2= textitRT or K(V22 - V12)=R(T2 - T1) ∴ W=(R/2)(T2 - T1)

Q. One mole of an ideal gas at temperature $T_{1}$ expands according to the law $(P / V)$ = constant. Find the work done when the final temperature becomes $T_{2}$ .

$R (T_{2} - T_{1})$

$(R /2) (T_{2} - T_{1})$

$(R /4) (T_{2} - T_{1})$

$P V (T_{2} - T_{1})$

$W = \int_{V_{1}}^{V_{2}} P d V = \int_{V_{1}}^{V_{2}} K V d V$ $(∵ \frac{p}{V} = K = constant)$
$∴ W = \frac{1}{2} k (V_{2}^{2} - V_{1}^{2})$
$P V = RT$
But $P = RT$
$∴ KV^{2} = RT$
or $K (V_{2}^{2} - V_{1}^{2}) = R (T_{2} - T_{1})$
$∴ W = \frac{R}{2} (T_{2} - T_{1})$

Q. One mole of an ideal gas at temperature T1​ expands according to the law (P/V) = constant. Find the work done when the final temperature becomes T2​ .

R(T2​−T1​)

(R/2)(T2​−T1​)

(R/4)(T2​−T1​)

PV(T2​−T1​)