An iron rod of heat capacity C is heated to temperature 8T_0 . It is then put in a cylindrical vesse

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11.Thermodynamics

hard

An iron rod of heat capacity $C$ is heated to temperature $8T_0$ . It is then put in a cylindrical vessel of adiabatic walls having two moles of air which can be treated as diatomic ideal gas at temperature $T_0$ and closed by a movable piston which is also adiabatic. The atmospheric pressure is $P_0$ . The cylinder with the piston combined have heat capacity $2C$ . Find the equilibrium temperature . (Assume temperature of air to be uniform and equal to vessel at all times) .

$\left( {\frac{{8C\ +\ 7R}}{{3C\ +\ 7R}}} \right){T_0}$

$\left( {\frac{{10C\ +\ 7R}}{{C\ +\ 7R}}} \right){T_0}$

$\left( {\frac{{8C\ +\ 7R}}{{C\ +\ 7R}}} \right){T_0}$

$\left( {\frac{{10C\ +\ 7R}}{{3C\ +\ 7R}}} \right){T_0}$

Solution

$\mathrm{C}\left(8 \mathrm{T}_{0}-\mathrm{T}\right)=2 \mathrm{C}\left(\mathrm{T}-\mathrm{T}_{0}\right)+2 \times \frac{7 \mathrm{R}}{2}\left(\mathrm{T}-\mathrm{T}_{0}\right)$

Standard 11

Physics

When a gas expands adiabatically

easy

Adiabatic modulus of elasticity of a gas is $2.1 \times {10^5}N/{m^2}.$ What will be its isothermal modulus of elasticity $\left( {\frac{{{C_p}}}{{{C_v}}} = 1.4} \right)$

medium

Figure shows a cylindrical adiabatic container of total volume $2V_0$ divided into two equal parts by a conducting piston (which is free to move). Each part containing identical gas at pressure $P_0$ . Initially temperature of left and right part is $4T_0$ and $T_0$ respectively. An external force is applied on the piston to keep the piston at rest. Find the value of external force required when thermal equilibrium is reached. ( $A =$ Area of piston)

hard

A polyatomic gas $\left( {\gamma = \frac{4}{3}} \right)$ is compressed to $\frac{1}{8}$ of its volume adiabatically. If its initial pressure is ${P_o}$, its new pressure will be

medium

What is an adiabatic process ? Derive an expression for work done in an adiabatic process.

medium

Solution

Similar Questions

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