A copper block of mass 2.5 kg is heated in a furnace to a temperature of 500 °C and then placed on a large ice block. What is the maximum amount of ice that can melt? (Specific heat of copper = $0.39 J g^{-1} K^{-1}$; heat of fusion of water = $335 J g^{-1}$ ).

Explain why : (b) a brass tumbler feels much colder than a wooden tray on a chilly day

Answer the following questions based on the P-T phase diagram of carbon dioxide: (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 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 = $0.91 J g^{-1} K^{-1}$.

Explain why : (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

The coefficient of volume expansion of glycerine is $49 \times 10^{-5} K^{-1}$. What is the fractional change in its density for a 30 °C rise in temperature ?

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 specific heat of the metal ?

Answer the following questions based on the P-T phase diagram of carbon dioxide: (b) What is the effect of decrease of pressure on the fusion and boiling point of $CO_2$ ?

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 = $2.0 \times 10^{-5} K^{-1}$, steel = $1.2 \times 10^{-5} K^{-1}$ ).

A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27.0 °C. What is the change in the diameter of the hole when the sheet is heated to 227 °C? Coefficient of linear expansion of copper = $1.70 \times 10^{-5} K^{-1}$.

Answer the following : (c) The absolute temperature (Kelvin scale) $T$ is related to the temperature $t_c$ on the Celsius scale by $t_c = T – 273.15$. Why do we have 273.15 in this relation, and not 273.16 ?

Answer the following : (d) What is the temperature of the triple-point of water on an absolute scale whose unit interval size is equal to that of the Fahrenheit scale ?

A large steel wheel is to be fitted on to a shaft of the same material. At 27 °C, the outer diameter of the shaft is 8.70 cm and the diameter of the central hole in the wheel is 8.69 cm. The shaft is cooled using ‘dry ice’. At what temperature of the shaft does the wheel slip on the shaft? Assume coefficient of linear expansion of the steel to be constant over the required temperature range : $\alpha_{steel} = 1.20 \times 10^{-5} K^{-1}$.

Answer the following questions based on the P – T phase diagram of $CO_2$: (a) $CO_2$ at 1 atm pressure and temperature – 60 °C is compressed isothermally. Does it go through a liquid phase ?

A steel tape 1m long is correctly calibrated for a temperature of 27.0 °C. The length of a steel rod measured by this tape is found to be 63.0 cm on a hot day when the temperature is 45.0 °C. What is the actual length of the steel rod on that day ? What is the length of the same steel rod on a day when the temperature is 27.0 °C ? Coefficient of linear expansion of steel = $1.20 \times 10^{-5} K^{-1}$.

Explain why : (a) a body with large reflectivity is a poor emitter

Two absolute scales A and B have triple points of water defined to be 200 A and 350 B. What is the relation between $T_A$ and $T_B$ ?

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 = $2256 \times 10^3 J kg^{-1}$.

Two ideal gas thermometers A and B use oxygen and hydrogen respectively. The following observations are made :
Temperature Pressure thermometer A Pressure thermometer B
Triple-point of water $1.250 \times 10^5$ Pa $0.200 \times 10^5$ Pa
Normal melting point of sulphur $1.797 \times 10^5$ Pa $0.287 \times 10^5$ Pa
(a) What is the absolute temperature of normal melting point of sulphur as read by thermometers A and B ?

Two ideal gas thermometers A and B use oxygen and hydrogen respectively. The following observations are made :
Temperature Pressure thermometer A Pressure thermometer B
Triple-point of water $1.250 \times 10^5$ Pa $0.200 \times 10^5$ Pa
Normal melting point of sulphur $1.797 \times 10^5$ Pa $0.287 \times 10^5$ Pa
(b) What do you think is the reason behind the slight difference in answers of thermometers A and B ? (The thermometers are not faulty). What further procedure is needed in the experiment to reduce the discrepancy between the two readings ?