Write the dimension formula of molar specific heat. Let the dimension formula of mole be [μ].

The dimensional formula for molar specific heat is, 

space space space space space space space open square brackets straight M to the power of 1 straight L squared straight T to the power of negative 2 end exponent straight K to the power of negative 1 end exponent straight mu to the power of negative 1 end exponent close square brackets


Explain why
(b) The coolant in a chemical or a nuclear plant (i.e., the liquid used to prevent the different parts of a plant from getting too hot) should have high specific heat.

(b) High specific heat capacity is required because the heat absorbed by a substance is directly proportional to the specific heat of the substance. Thus the coolant will work more effectively. 

Explain why?
(c) Air pressure in a car tyre increases during driving.

During driving, due to motion of the car the temperature of air inside the tyre increases.

According to Charle's law, 
P ∝T. 

Therefore, air pressure inside the tyre increases.

Explain why

(a) Two bodies at different temperatures T1 and T2 if brought in thermal contact do not necessarily settle to the mean temperature (T1 + T2)/2.

When two bodies are in thermal contact, heat flows from the body at higher temperature to the body at lower temperature till temperatures becomes equal.

The final temperature can be the mean temperature
fraction numerator straight T subscript 1 space plus space straight T subscript 2 over denominator 2 end fraction, only when thermal capacities of the two bodies are equal.

A geyser heats water flowing at the rate of 3.0 litres per minute from 27 °C to 77 °C. If the geyser operates on a gas burner, what is the rate of consumption of the fuel if its heat of combustion is 4.0 × 104 J/g? 

Water is flowing at a rate of 3.0 litre/min

The geyser heats the water, raising the temperature from 27°C to 77°C. 

Initial temperature, T1 = 27°C 

Final temperature, T2 = 77°C 

Rise in temperature, ΔT = T2 – T

                                      = 77 – 27

                                      = 50°C 

Heat of combustion = 4 × 104 J/g 

Specific heat of water, c = 4.2 J g–1 °C–1 

Mass of flowing water, m = 3.0 litre/min

                                     = 3000 g/min 

Total heat used, ΔQ = mc Δ

                             = 3000 × 4.2 × 50 

                             = 6.3 × 10J/min 


Rate of consumption =
open parentheses fraction numerator 6.3 space cross times space 10 to the power of 5 over denominator 4 space cross times space 10 to the power of 4 end fraction close parentheses space 

                                =  15.75 g/min.

What amount of heat must be supplied to 2.0 × 10–2 kg of nitrogen (at room temperature) to raise its temperature by 45 °C at constant pressure? (Molecular mass of N2 = 28; R= 8.3 J mol–1 K–1.)

Mass of nitrogen, m = 2.0 × 10–2 kg = 20 g

Rise in temperature, ΔT = 45°C

Molecular mass of N2M = 28 

Universal gas constant, R = 8.3 J mol–1 K–1 

Number of moles, n = straight m over straight M

                              = (fraction numerator 2 space cross times space 10 to the power of negative 2 end exponent space cross times space 10 cubed over denominator 28 end fraction)

                              = 0.714 

Molar specific heat at constant pressure for nitrogen,

p = 7 over 2 R

    = 7 over 2 × 8.3 

    = 29.05 J mol-1 K-1 

The total amount of heat to be supplied is given by the relation, 

ΔQ = nCΔ

     = 0.714 × 29.05 × 45 

     = 933.38 J 

Therefore, the amount of heat to be supplied is 933.38 J.