please solve this thermodynamics question . thank you.

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(1)(1){:[" ertics at "c_(p)=0.84(kJ)/(kgk)],[beta=1.2 xx10^(-3)k^(-1)quad1590(kg)/(m^(3))],[rho=(m)/(rho)=(5(kg))/(1590(kg)/(m^(3)))],[v_(1)=(1)/(c_(1))],[v_(1)=3.14465 xx10^(-3)m^(3)]:}let V=V(T,P)dV=((del V)/(del T))_(P)dT+((del V)/(del P))_(T)dPP is constant. P=1 bar{:[dv=((del V)/(del T))_(p)dT+0],[dv=((del V)/(del T))_(p)dT=-(2)]:}(2)We know that -volume expensivity beta=(1)/(V)((del V)/(del T))_(p)-(3)from Eepsi^(n)(2) and (3) -{:[d^(r)=beta vdT],[(dV)/(V)=beta dT],[int_(V1)^(v_(2))(dV)/(V)=betaint_(T_(1))^(T_(2))dT],[[ln v]_(V_(1))^(v_(2))=beta[T]_(T_(1))^(T_(2))],[ln v_(2)-ln v_(1)=beta(T_(2)-T_(1))],[ln (v_(2))/(V_(1))=beta(T_(2)-T_(1))]:}{:[ln (v_(2))/(v_(1))=(1.2 xx10^(-3)k^(-1)) ... See the full answer