A 10 kW drilling machine is used to drill a bore in a small aluminium block of mass 8.0 kg. How much is the rise in temperature of the block in 2.5 minutes, assuming 50% of power is used up in heating the machine itself or lost to the surroundings. Specific heat of aluminium = 0.91 J g^{–1} K^{–1}.

Asked by Abhisek | 1 year ago | 79

Power = 10 kW

Mass of the small aluminium block, m = 8 kg

= 8 x 10^{3} g

Time = 2.5×60=150 s

Specific heat of aluminium, c= 0.91 J g^{–1} K^{–1}.

Total energy =P×t=10^{4} ×150=15×10^{5} J

As 50% of the energy is used in the heating or lost to the surrounding,

Therefore, thermal energy available,

ΔQ= (\( \dfrac{1}{2}\)) x 15×10^{5}

= 7.5 x 10^{5}

As ΔQ=mcΔT

ΔT=\( \dfrac{ ΔQ}{mc}\)

= \(\dfrac{7.5 \times 10^5}{(8 \times 10^3 ×0.91)}\)

= \( \dfrac{7.5 \times 10^5}{7.28 \times 10^3}\)

= 1.03 x 10^{2 }

Rise in the temperature of the block, ΔT = 103°C

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}.