The electrical resistance in ohms of a certain thermometer varies with temperature according to the approximate law:

$\mathrm{R}={\mathrm{R}}_0\left[1+\mathrm{\alpha }\left(\mathrm{T}-{\mathrm{T}}_0\right)\right]$

The resistance is 101.6 Ω at the triple-point of water 273.16 K, and 165.5 Ω at the normal melting point of lead (600.5 K). What is the temperature when the resistance is 123.4 Ω?

$\left(1\right) 384.8 \mathrm{K}$
$\left(2\right) 486.8 \mathrm{K}$
$\left(3\right) 287.61 \mathrm{K}$
$\left(4\right) 185.61 \mathrm{K}$

A steel tape \(1\) m long is correctly calibrated for a temperature of \(27^\circ \text{C}\). 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 \(45^\circ \text{C}\). What is the actual length of the steel rod on that day?
(Coefficient of linear expansion of steel = \(1.20\times 10^{-5}~\text{K}^{-1}\)).
1. \( 62.485 \) cm
2. \( 60.762 \) cm
3. \( 65.935 \) cm
4. \( 63.013\) cm

A large steel wheel is to be fitted onto a shaft of the same material. At 27 °C, the outer diameter of the shaft is 8.70 cm and the wheel's central hole has a diameter of 8.69 cm. The shaft is cooled using ‘dry ice’. At what temperature of the shaft does the wheel slip on the shaft?
(Assume the coefficient of linear expansion of the steel to be constant over the required temperature range  and \(\alpha\) steel = \(1.20 \times 10^{-5} K^{-1}\))
1. 68°C
2. -70°C
3.  -69°C
4. -67°C

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?

(Co-efficient of linear expansion of copper= $1.70\times {10}^{-5} {\mathrm{K}}^{-1}$)

1. 0.0144 cm
2. 0.0234 cm
3. 0.0123 cm
4. 0.0111 cm

A brass wire \(1.8~\text m\) long at \(27^\circ \text C\) is held taut with a little tension between two rigid supports. If the wire is cooled to a temperature of \(-39^\circ \text C,\) what is the tension created in a wire with a diameter of \(2.0~\text{mm}?\)  
(coefficient of linear expansion of brass \(=2.0 \times10^{-5}~\text{K}^{-1},\) Young's modulus of brass\(=0.91 \times10^{11}~\text{Pa}\) )
1. \(3.8 \times 10^3~\text N\) 
2. \(3.8 \times 10^2~\text N\) 
3. \(2.9 \times 10^{-2}~\text N\) 
4. \(2.9 \times 10^{2}~\text N\) 

The coefficient of volume expansion of glycerine is \(49\times 10^{-5}\) K^–1. What is the fractional change in its density for a \(30^\circ \text{C}\) rise in temperature?
1. \(1.44\times10^{-3}\)
2. \(1.57\times10^{-3}\)
3. \(1.57\times10^{-2}\)
4. \(1.44\times10^{-2}\)

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 $=0.91 J g^{-1} K^{-1}$.)
1. 103°C
2. 109°C
3. 211°C
4. 197°C

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 = $0.39 J g^{-1} K^{-1},$ the heat of fusion of water = 335 J/g)

1. 1.32 kg
2. 1.12 kg
3. 1.45 kg
4. 1.53 kg