Thermodynamics PYQ — Page 9

Two metallic blocks ${M}_{1}$ and ${M}_{2}$ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of ${M}_{2}$ is $K$ then the thermal conductivity of ${M}_{1}$ will be : [Assume steady state heat conduction] 

When a gas filled in a closed vessel is heated by raising the temperature by $1^{\circ}C$, its pressure increases by $0.4%$ The initial temperature of the gas is _____ $K$.

A mixture of hydrogen and oxygen has volume $2000{\mathrm{cm}}^{3}$, temperature $300K$, pressure $100\mathrm{kPa}$ and mass $0.76g$. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be [Take gas constant $R=8.3J{K}^{-1}{\mathrm{mol}}^{-1}$]

A lead bullet penetrates into a solid object and melts. Assuming that $40%$ of its kinetic energy is used to heat it, the initial speed of bullet is (Given, initial temperature of the bullet $=127^{\circ}C$, Melting point of the bullet $=327^{\circ}C$, Latent heat of fusion of lead $=2.5\times {10}^{4}J{\mathrm{kg}}^{-1}$, Specific heat capacity of lead $=125J\mathrm{kg}{K}^{-1}$)

A unit scale is to be prepared whose length does not change with temperature and remains $20\mathrm{cm}$, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is $40\mathrm{cm}$ and length of iron will be _____ $\mathrm{cm}$. $({\alpha }_{\mathrm{iron}}=1.2\times {10}^{-5}{K}^{-1}$ and ${\alpha }_{\mathrm{brass}}=1.8\times {10}^{-5}{K}^{-1})$.

For a perfect gas, two pressures ${P}_{1}$ and ${P}_{2}$ are shown in figure. The graph shows 

A solid metallic cube having total surface area $24{m}^{2}$ is uniformly heated. If its temperature is increased by $10^{\circ}C$, calculate the increase in volume of the cube. (Given $\alpha =5.0\times {10}^{-4}{C\circ }^{-1}$).

If ${K}_{1}$ and ${K}_{2}$ are the thermal conductivities ${L}_{1}$ and ${L}_{2}$ are the lengths and ${A}_{1}$ and ${A}_{2}$ are the cross sectional areas of steel and copper rods respectively such that $\frac{{K}_{2}}{{K}_{1}}=9,\frac{{A}_{1}}{{A}_{2}}=2,\frac{{L}_{1}}{{L}_{2}}=2$. Then, for the arrangement as shown in the figure. The value of temperature $T$ of the steel - copper junction in the steady state will be 

Resistance of the wire is measured as $2\Omega$ and $3\Omega$ at $10^{\circ}C$ and $30^{\circ}C$ respectively. Temperature coefficient of resistance of the material of the wire is

As per the given figure, two plates $A$ and $B$ of thermal conductivity $K$ and $2K$ are joined together to form a compound plate. The thickness of plates are $4.0\mathrm{cm}$ and $2.5\mathrm{cm}$ respectively and the area of cross-section is $120{\mathrm{cm}}^{2}$ for each plate. The equivalent thermal conductivity of the compound plate is $(1+\frac{5}{\alpha })K$, then the value of $\alpha$ will be _____ . 

At a certain temperature, the degrees of freedom per molecule for gas is $8$. The gas performs $150J$ of work when it expands under constant pressure. The amount of heat absorbed by the gas will be _____ $J$.

A cylinder of fixed capacity of $44.8$ litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by $20.0^{\circ}C$ will be (Given gas constant $R=8.3J{K}^{-1}{\mathrm{mol}}^{-1}$)

Given below are two statements: Statement I :The average momentum of a molecule in a sample of an ideal gas depends on temperature. Statement II : The rms speed of oxygen molecules in a gas is $v$. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become $2v$. In the light of the above statements, choose the correct answer from the options given below :

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is $\frac{{\alpha }^{2}}{4}RJ\mathrm{mol}{K}^{-1}$; then the value of $\alpha$ will be _____ . (Assume that the given diatomic gas has no vibrational mode.)

$0.056\mathrm{kg}$ of Nitrogen is enclosed in a vessel at a temperature of $127^{\circ}C$. The amount of heat required to double the speed of its molecules is_____ $\mathrm{kcal}$. (Take $R=2\mathrm{cal}\mathrm{mole}{K-1}^{-1}$ )

An ice cube of dimensions $60\mathrm{cm}\times 50\mathrm{cm}\times 20\mathrm{cm}$ is placed in an insulation box of wall thickness $1\mathrm{cm}$. The box keeping the ice cube at $0^{\circ}C$ of temperature is brought to a room of temperature $40^{\circ}C$. The rate of melting of ice is approximately: (Latent heat of fusion of ice is $3.4\times {10}^{5}J{\mathrm{kg}}^{-1}$ and thermal conducting of insulation wall is $0.05W{m}^{-1}^{\circ}{C}^{-1}$)

A certain amount of gas of volume $V$ at $27^{\circ}C$ temperature and pressure $2\times {10}^{7}N{m}^{-2}$ expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use $\gamma =1.5$)

A flask contains argon and oxygen in the ratio of $3:2$ in mass and the mixture is kept at $27^{\circ}C$. The ratio of their average kinetic energy per molecule respectively

A copper block of mass $5.0\mathrm{kg}$ is heated to a temperature of $500^{\circ}C$ and is placed on a large ice block. What is the maximum amount of ice that can melt? [Specific heat of copper : $0.39{\mathrm{Jg}}^{-1}{C\circ }^{-1}$ and latent heat of fusion of water : $335{\mathrm{Jg}}^{-1}$]

A block of ice of mass $120g$ at temperature $0^{\circ}C$ is put in $300g$ of water at $25^{\circ}C$. The $xg$ of ice melts as the temperature of the water reaches $0^{\circ}C$. The value of $x$ is [Use: Specific heat capacity of water $=4200J{\mathrm{kg}}^{-1}{K}^{-1}$, Latent heat of ice $=3.5\times {10}^{5}J{\mathrm{kg}}^{-1}$]

The total internal energy of two mole monoatomic ideal gas at temperature $T=300K$ will be _____ $J$. (Given $R=8.31J{\mathrm{mol}}^{-1}\cdot K$)

A vessel contains $16g$ of hydrogen and $128g$ of oxygen at standard temperature and pressure. The volume of the vessel in ${\mathrm{cm}}^{3}$ is :

The ratio of specific heats $(\frac{{C}_{P}}{{C}_{V}})$ in terms of degree of freedom $(f)$ is given by :

A monoatomic gas performs a work of $\frac{Q}{4}$ where $Q$ is the heat supplied to it. The molar heat capacity of the gas will be _____ $R$ during this transformation. Where $R$ is the gas constant.