Diameter of hole ( D_{1}) = 4.24 cm

Initial Temperature, T_{1} = 27.0°C = 27+ 273 = 300 K

Final temperature, T_{2} =227°C = 227+ 273 = 500K

Let the diameter of the hole at the final temperature be D_{2}

Coefficient of linear expansion of copper, α= 1.70 × 10^{–5} K^{–1}

Initial area of hole (A_{o})= πr² =π (\( \dfrac{4.24}{2}\))²

coefficient of superficial expansion (β)

= 2× coefficient of linear expansion of copper (α)

= 2 × 1.7 × 10^{-5 }= 3.4 × 10^{-5 }

Using the formula,

A = A_{o}( 1 + β∆T)

A = π (\( \dfrac{4.24}{2}\))² [1 + 3.4 × 10^{-5} × (500-300)]

= π (\( \dfrac{4.24}{2}\))² [ 1 + 3.4 × 10^{-5} × 200]

= π (\( \dfrac{4.24}{2}\))² [ 1 + 6.8 × 10^{-3} ]

= π (\( \dfrac{4.24}{2}\))² [ 1 + 0.0068]

= π (\( \dfrac{4.24}{2}\))² (1.0068)

\( \dfrac{πD_2^²}{4}\) = π (\( \dfrac{4.24}{2}\))² ( 1.0068 )

D_{2}²= 17.97 (1.0068)

D_{2}²= 18.092

= 4.253

D_{2} = 4.253 cm

Change in diameter (∆D) = D_{2} – D_{1}

= 4.253 – 4.24

= 0.013 cm

Answered by Pragya Singh | 1 year agoA 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}.