A gas expands with temperature according to the relation V=KT1/3.  What is the work done when the temperature changes by  30oC

V=KT1/3⇒   dV=13   KT−23  dT⇒   =13  VT1/3 T−23  dT⇒  dV =13  V.  T−1  dT⇒  dVV =13   dTT     ⇒   W=∫T2T1  RTT  dT=13   R  T2−T1⇒   W=13  ×  R  ×  30=10R