PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions

Can we define specific heat capacity for an adiabatic process?

Does a solid also have two kinds of molar heat capacities C_p and C_v? If yes, is C_p > C_v? Or is C_p − C_v = R?

Can a process on an ideal gas be both adiabatic and isothermal?

Show that the slope of the p−V diagram is greater for an adiabatic process compared to an isothermal process.

Can two states of an ideal gas be connected by an isothermal process as well as an adiabatic process?

In a room containing air, heat can go from one place to another

In an isothermal process on an ideal gas, the pressure increases by 0.5%. The volume decreases by about

Two samples A and B are initially kept in the same state. Sample A is expanded through an adiabatic process and the sample B through an isothermal process. The final volumes of the samples are the same. The final pressures in A and B are p_A and p_Brespectively.

Let ∆W_a and ∆W_b be the work done by the systems A and B, respectively, in the previous question.

Consider the processes A and B shown in the figure. It is possible that

Three identical adiabatic containers A, B and C contain helium, neon and oxygen, respectively, at equal pressure. The gases are pushed to half their original volumes.
(a) The final temperatures in the three containers will be the same.
(b) The final pressures in the three containers will be the same.
(c) The pressures of helium and neon will be the same but that of oxygen will be different.
(d) The temperatures of helium and neon will be the same but that of oxygen will be different.

5 g of a gas is contained in a rigid container and is heated from 15°C to 25°C. Specific heat capacity of the gas at constant volume is 0.172 cal g⁻¹ °C⁻¹ and the mechanical equivalent of heat is 4.2 J cal⁻¹. Calculate the change in the internal energy of the gas

A sample of air weighing 1.18 g occupies 1.0 × 10³ cm³ when kept at 300 K and 1.0 × 10⁵ Pa. When 2.0 cal of heat is added to it at constant volume, its temperature increases by 1°C. Calculate the amount of heat needed to increase the temperature of air by 1°C at constant pressure if the mechanical equivalent of heat is  4.2 × 10⁷ erg cal⁻¹. Assume that air behaves as an ideal gas.

An ideal gas expands from 100 cm³ to 200 cm³ at a constant pressure of 2.0 × 10⁵ Pa when 50 J of heat is supplied to it. Calculate (a) the change in internal energy of the gas (b) the number of moles in the gas if the initial temperature is 300 K (c) the molar heat capacity C_p at constant pressure and (d) the molar heat capacity C_v at constant volume.

A mixture  contains 1 mole of helium (C_p = 2.5 R, C_v = 1.5 R) and 1 mole of hydrogen (C_p= 3.5 R, C_v = 2.5 R). Calculate the values of C_p, C_v and γ for the mixture.

In Joly's differential steam calorimeter, 3 g of an ideal gas is contained in a rigid closed sphere at 20°C. The sphere is heated by steam at 100°C and it is found that an extra 0.095 g of steam has condensed into water as the temperature of the gas becomes constant. Calculate the specific heat capacity of the gas in J g⁻¹ K⁻¹. The latent heat of vaporisation of water = 540 cal g⁻¹ 

One end of a steel rod (K = 46 J s⁻¹ m⁻¹°C⁻¹) of length 1.0 m is kept in ice at 0°C and the other end is kept in boiling water at 100°C. The area of cross section of the rod is 0.04 cm². Assuming no heat loss to the atmosphere, find the mass of the ice melting per second. Latent heat of fusion of ice = 3.36 × 10⁵ J kg⁻¹.

Air (γ = 1.4) is pumped at 2 atm pressure in a motor tyre at 20°C. If the tyre suddenly bursts, what would be the temperature of the air coming out of the tyre? Neglect any mixing with the atmospheric air.

A steel frame (K = 45 W m⁻¹°C⁻¹) of total length 60 cm and cross sectional area 0.20 cm², forms three sides of a square. The free ends are maintained at 20°C and 40°C. Find the rate of heat flow through a cross section of the frame.