The slopes of the isothermal and adiabatic $p-V$ graphs of a gas are $S_I$ and $S_A$ respectively. If the heat capacity ratio of the gas is $\frac{3}{2}$,then $\frac{S_I}{S_A}=$

$A$ gas is compressed from a volume of $2 \,m^3$ to a volume of $1 \,m^3$ at a constant pressure of $100 \,N m^{-2}$. Then it is heated at constant volume by supplying $150 \,J$ of energy. As a result,the internal energy of the gas

When a system is taken from state $i$ to state $f$ along the path $iaf$,$Q = 50 \ J$ and $W = 20 \ J$. Along the path $ibf$,$Q = 35 \ J$ and $W = -13 \ J$. For the curved path $fi$,$Q = \dots \ J$.

When $80 \ J$ of heat is supplied to a gas at constant pressure,if the work done by the gas is $20 \ J$,then the ratio of the specific heat capacities of the gas is

Three samples of the same gas $A, B$ and $C$ $(\gamma = 3/2)$ have initially equal volume. Now the volume of each sample is doubled. The process is adiabatic for $A$,isobaric for $B$,and isothermal for $C$. If the final pressures are equal for all three samples,the ratio of their initial pressures is:

$A$ gas is compressed from a volume of $2\,m^3$ to a volume of $1\,m^3$ at a constant pressure of $100\,N/m^2$. Then it is heated at constant volume by supplying $150\,J$ of energy. As a result,the internal energy of the gas