Heat and Thermodynamics

A heat source at T = 10³ K is connected to another heat reservoir at T = 10² K by a copper slab which is 1 mthick. Given that the thermal conductivity of copper is 0.1 WK^–1m^–1, the energy flux through it in the steady state is -

A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is K₁ and the of the outer cylinder is K₂. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is :

A cylinder with fixed capacity of 67.2 lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20°C is : [Given that R = 8.31 J mol^–1 K^–1]

In thermodynamics, heat and work are :

The root mean square speed of smoke particles of mass $5 \times 10^{-17} \mathrm{~kg}$ in their Brownian motion in air at NTP is approximately. [Given $\mathrm{k}=1.38 \times 10^{-23} \mathrm{JK}^{-1}$]

A vessel contains 16g of hydrogen and 128g of oxygen at standard temperature and pressure. The volume of the vessel in cm³ is :

When M₁ gram of ice at –10^oC (specific heat = 0.5 cal g^–1 ^oC^–1 ) is added to M₂ gram of water at 50C, finally no ice is left and the water is at 0°C. The value of latent heat of ice, in cal g^–1 is :

An electric appliance supplies 6000 J/min heat to the system. If the system delivers a power of 90W. How long it would take to increase the internal energy by 2.5 $\times$ 10³ J ?

A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT) of the mixture is :

Match the ${{{C_P}} \over {{C_V}}}$ ratio for ideal gases with different type of molecules : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-baqh{text-align:center;vertical-align:top} .tg .tg-0lax{text-align:left;vertical-align:top} Molecule Type C_P/C_V (A) Monatomic (I) 7/5 (B) Diatomic rigid molecules (II) 9/7 (C) Diatomic non-rigid molecules (III) 4/3 (D) Triatomic rigid molecules (IV) 5/3

Two ideal polyatomic gases at temperatures T₁ and T₂ are mixed so that there is no loss of energy. If F₁ and F₂, m₁ and m₂, n₁ and n₂ be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is :

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: If $d Q$ and $d W$ represent the heat supplied to the system and the work done on the system respectively. Then according to the first law of thermodynamics $d Q=d U-d W$. Reason R: First law of thermodynamics is based on law of conservation of energy. In the light of the above statements, choose the correct answer from the options given below:

One $kg$ of a diatomic gas is at a pressure of $8 \times {10^4}\,N/{m^2}.$ The density of the gas is $4kg/{m^3}$. What is the energy of the gas due to its thermal motion ?

Three perfect gases at absolute temperatures ${T_1},\,{T_2}$ and ${T_3}$ are mixed. The masses of molecules are ${m_1},{m_2}$ and ${m_3}$ and the number of molecules are ${n_1},$ ${n_2}$ and ${n_3}$ respectively. Assuming no loss of energy, the final temperature of the mixture is:

An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure (C_p ) and at constant volume (C_v) is :

Two moles of helium are mixed with n moles of hydrogen. If ${{Cp} \over {Cv}} = {3 \over 2}$ for the mixture, then the value of n is :

A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. considering only translational and rotational modes, the total internal energy of the system is :

An ideal gas occupies a volume of 2m³ at a pressure of 3 $\times$ 10⁶ Pa. The energy of the gas is :