Calculate the value of mechanical equivalent of heat from the following data. Specific heat capacity of air at constant volume =`170 cal kg^(-1) K^(-1)` , `gamma = C_p/ C_v = 1.4` and the density of air at STP is `1.29 kg m^(-3)`. Gas constant `R = 8.3 JK^(-1) mol^(-1)`.

Answer

`[4.2 j//cal.]`

Explanation

Here, `c_(v)=170 cal//kg-K=0.17 cal//g-K`
As, `gamma=(c_(p))/(c_(v))`
`:. C_(p)=gamma c_(v)`
`c_(p)=1.4xx0.17=0.238 cal//g-K`
`As, c_(p)-c_(v)=(r)/(j)=(Pv)/(Tj)=(Pxx1//rho)/(Tj)`
`:. J=(P)/(rho T(c_(p)-c_(c)))=(1.01xx10^(6))/(1.29xx10^(-3)xx273xx0.068)`
`=4.2xx10^(7) erg//"calorie" =4.2 J//cal`