A brass rod of length 50 cm and diameter 3.0 mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250°C, if the original lengths are at 40.0°C? Is there a ‘thermal stress’ developed at the junction? The ends of the rod are free to expand (Co-efficient of linear expansion of brass = \( 2.0 × 10^{–5} K^{–1}\), steel = \( 1.2 × 10^{–5} K^{–1}\) ).
Length of the brass rod = length of the steel rod = L0 = 50 cm
Diameter of the brass rod = diameter of the steel rod = 3 mm
Initial temperature ( T1) = 40°C
Final temperature ( T2) = 250°C
Therefore, the increase in temperature (∆T)
= 250 – 40 =210°C
Coefficient of linear expansion of brass, ∝ = 2 × 10-5 K-1
Coefficient of linear expansion of steel, β = 1.2 × 10-5 K-1
Final length of brass, L1
L1 = Lo(1 + ∝∆T)
= 50( 1 + (2 × 10-5 × 210))
=50( 1 + 420 × 10-5)
= 50× 1.00420
= 50.21 cm
Increase in length of brass ( ∆L)
= L2 – L1
= 50.21 – 50
= 0.21 cm
Final length of steel, L2= Lo(1 + β∆T)
= 50( 1 + (1.2 × 10-5 × 210))
= 50 × 1.00252
= 50.126 cm
Increase in length ( ∆L’)
= 50.126 cm – 50 cm
= 0.126 cm
Total increase in the length = ∆L + ∆L’
= 0.21 + 0.126
= 0.336 cm
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 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.