One mole of monatomic ideal gas undergoes the thermodynamic process a arrow b as shown in the P-V diagram. During this process, the maximum temperature will occur when gas volume is (m/n) V0 . Find (m+n).

Question

One mole of monatomic ideal gas undergoes the thermodynamic process a arrow b as shown in the P-V diagram. During this process, the maximum temperature will occur when gas volume is (m/n) V0 . Find (m+n). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Equation of P V graph: P=-((P0/V0)) V+3 P0=m V+C (m=-P0 / V0. and C=3 P0 ) Putting this in ideal gas equation P V=n R T, we get m V2+C V=R T (∵ n=1) Differentiating above equation w.r.t. V, we get ⇒ 2 m V+C=R (d T/d V) For T max , (d T/d V)=0 ⇒ V=-(C/2 m)=(3 V0/2)

Q. One mole of monatomic ideal gas undergoes the thermodynamic process a→b as shown in the P−V diagram. During this process, the maximum temperature will occur when gas volume is nm​V0​. Find (m+n).

Equation of PV graph: P=−(V0​P0​​)V+3P0​=mV+C (m=−P0​/V0​ and C=3P0​ ) Putting this in ideal gas equation PV=nRT, we get mV2+CV=RT(∵n=1) Differentiating above equation w.r.t. V, we get ⇒2mV+C=RdVdT​ For Tmax​,dVdT​=0 ⇒V=−2mC​=23V0​​

Q. One mole of monatomic ideal gas undergoes the thermodynamic process $a \to b$ as shown in the $P - V$ diagram. During this process, the maximum temperature will occur when gas volume is $\frac{m}{n} V_{0} .$ Find $(m + n)$ .