## Assignments thermal properties of matter

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**Assignments**
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**Q. 1 **the triple points of neon and carbon dioxide are 24.57 k and 216.55K respectively. Express these temperatures on Celsius and Fahrenheit scales

**Q.2** Two absolute scales A and B have triple points of water defined as 200A and 350A. What is the relation between T_{A} and T_{B}

**Q.3**The pressure of the gas in constant volume gas thermometer are 80 cm, 90 cm and 100 cm of mercury at the ice point, the steam point and in a heated wax bath respectively. Find the temperature of the wax bath.

**Q. 4. **A resistance thermometer reads R= 20.0Ω, 27.5Ω and 50.0 Ω at the ice point (0°C), the steam point (100°C) and the zinc point 420°C respectively. Assuming that the resistance varies with temperature as R_{θ}=R_{0}(1+αθ+βθ^{2}), find the values of R_{0}, α and β. Here θ represents temperature on Celsius scale.

**Q.5**A circular hole of diameter 2.00 cm is made in an aluminum plate at 0°C. What will be the diameter at 100°C. α for aluminum = 2.3 × 10^{-3} °C^{-1}.

**Q. 6**The density of water at 0°C is 0.998 gm/cm^{3} and at 4°C is 1.000 gm/cm^{3}. Calculate the average coefficient of volume expansion of water in temperature range 0 to 4°C.

**Q. 7**A pendulum clock gives correct time at 20°C at a place where g=9.8m/ s^{2}. The pendulum consists of a light steel rod connected to a heavy ball. It is taken to a different place where of = 9.788m/s^{2}. At what temperature will it give correct time? Coefficient of linear expansion of steel = 12X10^{-6}°C^{-1}.

**Q 8** A glass vessel measures exactly 10cm × 10cm × 10cm at 0°C. It is filled completely with mercury at this temperature. When the temperature rises to 10°C , 1.6 cm^{3} of mercury overflows. Calculate the Coefficient of volume of mercury. Coefficient of linear expansion of glass = 6.5 × 10^{-6}°C^{-1}.

**Q 9** A steel rod is clamped at its two ends and rests on a fixed horizontal base. The rod is unstrained at 20°C. Find the longitudinal strain developed in the rod if temperature rises to 50°C. Coefficient of linear expansion of steel is 1.2 × 10^{-5}°C^{-1}

**Q 10**To ensure a light fit aluminum reverts used in airplane construction are made slightly larger than the revert holes and cooled by dry ice (solid CO_{2}) before being driven. If diameter of a hole is 0.2500 in, what should be the diameter of revert at 20°C if is diameter is equal to that of hole when revert is cooled to -78°C the temperature of dry ice? Coefficient of Linear expansion of Aluminum =2.4X10^{-5}°C^{-1}

**Q. 11**A steel ring of 3.000 in inside diameter at 20°C is to be heated and slipped over a brass shaft measuring 3.002 inch in diameter at 20°C α_{brass} = 2 × 10^{-5} °C^{-1} α_{steel} =1.2 × 10^{-5} °C^{-1}

(a) To what temperature should the ring be heated?

(b) If the ring and shaft together are cooled by some means such as liquid air, at what temperature will the ring just slip off the shaft.

**Q 12**A metal rod 30.0 cm long expands by 0.075 cm when its temperature is raised from 0°C to 100°C.A rod of a different metal and of same length expands by 0.045 cm for the same raise in temperature. A third rod also 30.0 cm long is made up of the pieces of each of the above metals placed and to end. and expends 0.065 cm between 0°C and 100°C. Find the length of each portion of the composite bar.

**Q 13**Suppose that a steel hoop could be constructed around the earth's equator, just fitting it at a temperature 20°C. What would be the thickness of space between hoop and the earth if the temperature of the hoop were increased by 1 °C.

α_{steel} = 1.2 × 10^{-5} °C^{-1}

**Q 14**Two brass rods and one steel rod of equal length L_{0} and equal crossectional are joined rigidly at their ends .All rods are in the state of zero tension at 0° C. Find the length of the system when the temperature is increased to θ.

Coefficient of linear expansion of steel=α_{s}

Coefficient of linear expansion of brass=α_{b}

Young modulus of steel=Y_{s}

Young modulus of brass=Y_{b}

**Q 15** What will the length of steel and copper rod .So that length of steel rod is 5cm longer then the copper rod at all the temperature (α_{copper}=1.7X10^{-5} /C,α_{steel}=1.1X10^{-5} /C)

**Q 16**A bimetallic strip is formed out of two identical strips .One of the copper and other of brass. The coefficient of linear expansion of the two metals are α_{c} and α_{B}.On heating the strip through the temperature change ΔT,the strip bends into an arc of the circle. Find the radius of the curvature of the strip

**Q 17** Show that the moment of inertia of the solid body of any shape changes with the temperature as I=I_{0}(1+2αθ) .Where I_{0} is the moment of inertia at 0° C and α coefficient of linear expansion of the solid

**Q 18** A aluminum container of mass .65 kg contains .35kg of water at 18° C.A block of iron of mass .2kg at 100° C is put into the water. Find the equilibrium temperature of the mixture. Specific heat capacities of aluminum ,iron and water are 910 J/Kg-K,470J/kg-K and 4200 J/kg-K resp.

**Q 19** An iron piece of mass 200 gm is kept inside a furnace for a considerable long time and then put in calorimeter of water equivalent 20 Gm containing 280 gm of water at 22° C. The mixture attains an equilibrium temperature of 80° C. Find the temperature of the furnace.

Specific heat capacities of iron 470 J/kg-° C.

**Q20** 1 kg of ice at 0 °C is mixed with 1 kg of steam at 100 °C. What will be the composition of the system when thermal equilibrium is reached. latent heat of fusion of ice = 3.36X10^{5} J/kg and latent heat of vaporization of water = 2.26X10^{6} J/kg.

**Q 21** A bullet of mass 30 gm. enters into a fixed wooden block with a speed 50 m / s and stops in it. Calculate the change in internal energy during this process.

**Q 22** An animal of 70 kg is running with a speed of 6 m/s. If all the KE of animal can be used in increasing water from 18 °C to 32 °C, how much water can be heated with this energy

**Q 23** A copper cube of mass 300g slides down on a rough inclined plane of inclination 40 ° at a constant speed. Assume that any loss in mechanical energy goes into copper block as thermal energy find the increase in thermal energy of the block as it slides down through 50 cm. specific heat capacity of copper = 420J/kg-k.
**Solutions **
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