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

1 Answer

Solution :-

Power = 10 kW

Mass of the small aluminium block, m = 8 kg

= 8 x 103 g

Time = 2.5×60=150 s

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

Total energy =P×t=104 ×150=15×105 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 15×105

= 7.5 x 105

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

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

Answered by Pragya Singh | 1 year ago

Related Questions

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?

Class 11 Physics Thermal Properties of Matter View Answer

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?

Class 11 Physics Thermal Properties of Matter View Answer

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.

Class 11 Physics Thermal Properties of Matter View Answer

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

Class 11 Physics Thermal Properties of Matter View Answer

A brass boiler has a base area of 0.15 m2 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 × 103 J kg–1.

Class 11 Physics Thermal Properties of Matter View Answer