In an experiment on the specific heat of a metal, a 0.20 kg block of the metal at 150°C is dropped in a copper calorimeter (of water equivalent 0.025 kg) containing \( 150 cm^3\) of water at 27 °C. The final temperature is 40°C. Compute the specific heat of the metal. If heat losses to the surroundings are not negligible, is your answer greater or smaller than the actual value for the specific heat of the metal?

Asked by Abhisek | 1 year ago | 134

Mass of the metal block, m = 0.20 kg = 200 g

Initial temperature of the metal block, T_{1} = 150°C

Final temperature of the metal block, T_{2} = 40°C

Copper calorimeter has water equivalent of mass, m_{1}= 0.025 kg

= 25 g

Volume of water, V = 150 cm^{3}

Mass (M) of water at temperature T = 27°C is 150×1

=150g

Specific heat of water, C_{w}=4.186J/g/K

Specific heat of the metal = c

Decrease in the temperature of the metal block

ΔT_{1}=T_{1}–T_{2}_{ }=150−40=110°C

Increase in the temperature of the water and calorimeter system,

ΔT_{2}=40−27=13°C

Heat lost by the metal

= Heat gained by the water + heat gained by the calorimeter

mCΔT_{1} = (M+m_{1})C_{w}ΔT_{2}

C =\( \dfrac{(M+m_1)C_wΔT_2}{mΔT_1}\)

= \( \dfrac{(150 +25) \times 4.186 \times 13}{(200 \times 100)}\)

=\( \dfrac{(175 \times 4.186 \times 13)}{(200 \times 100)}\)

= \(\dfrac{9523.15}{2200}\)

= 0.43 Jg^{−1}k^{−1}

A hot ball cools from 90°C to 10°C in 5 minutes. If the surrounding temperature is 20°C, what is the time taken to cool from 60°C to 30°C?

Answer the following questions based on the P-T phase diagram of carbon dioxide:

**(a)** At what temperature and pressure can the solid, liquid and vapour phases of \( CO_2\) co-exist in equilibrium?

**(b)** What is the effect of the decrease of pressure on the fusion and boiling point of \( CO_2\)?

**(c) **What are the critical temperature and pressure for \( CO_2\)? What is its significance?

**(d)** Is \( CO_2\) solid, liquid or gas at

**(a) **–70°C under 1 atm,

**(b)** –60°C under 10 atm,

**(c) **15°C under 56 atm?

A body cools from 80°C to 50°C in 5 minutes. Calculate the time it takes to cool from 60°C to 30°C. The temperature of the surroundings is 20°C.

Explain why :

**(a)** a body with large reflectivity is a poor emitter

**(b)** a brass tumbler feels much colder than a wooden tray on a chilly day

**(c)** an optical pyrometer (for measuring high temperatures) calibrated for an ideal black body radiation gives too low a value for the temperature of a red hot iron piece in the open, but gives a correct value for the temperature when the same piece is in the furnace

**(d) **the earth without its atmosphere would be inhospitably cold

**(e)** heating systems based on the circulation of steam are more efficient in warming a building than those based on the circulation of hot water

A brass boiler has a base area of 0.15 m^{2} and thickness 1.0 cm. It boils water at the rate of 6.0 kg/min when placed on a gas stove. Estimate the temperature of the part of the flame in contact with the boiler. Thermal conductivity of brass = 109 J s^{–1} m^{–1 }K^{–1}; Heat of vaporisation of water = 2256 × 10^{3} J kg^{–1}.