Specific heat capacity

Show that the mass of the ice sculpture is about 2.210⁵kg.

density of ice = 920 kg m^–3

Give two reasons why your analysis of the situation may be incorrect.

The potential difference (p.d.) from a power pack alternates at a frequency of 50 Hz. The root-mean-square (r.m.s.) value of the output p.d. is measured to be 8.5 V using an a.c. voltmeter.

The output from the power pack is connected to a resistor of resistance 1.5 Ω.

Show that the rate of power dissipation in the resistor is about 48 W.

A lab technician used the resistor to heat 1.25 10^–4m³ of milk in a beaker.

Calculate the time taken for the milk to increase in temperature by 12 °C.

specific heat capacity of milk = 3930 J kg^–1K^–1

The lab technician used an oscilloscope to determine the supply frequency and check the r.m.s. output p.d. displayed by the voltmeter.

Describe the methods the technician should use.

Chocolate is a solid at room temperature, but melts just below body temperature.

A student investigated the viscosity of some melted chocolate using a falling-ball method. Since chocolate is opaque, a thin rod was attached to the ball so that the movement of the ball could be monitored. The apparatus is shown in the diagram.

The chocolate was maintained at a constant temperature during the investigation.

The student used a stopwatch to measure the time t for the ball to fall 22.5 cm whilst travelling at its terminal velocity v.

Her results are shown in the table.

v is given by the formula

where r is the radius of the ball

The graph is taken from a commercial website. It shows how, at the temperature of the experiment, η depends on the percentage of cocoa in the chocolate.

The chocolate wrapper indicated that the chocolate had a 35% cocoa content.

Assess whether the student’s timing data supports this percentage cocoa content.

r = 4.25×10^–3m

Explain one reason why the student’s data may have led to an inaccurate conclusion about the cocoa content.

One type of chocolate melts at a temperature of 32C.

The energy released when 65 g of this chocolate is digested is 345 kcal.

It is suggested that the energy used to melt a piece of this chocolate is at least 15% of the energy released when the chocolate is digested.

Assess the accuracy of this suggestion.

initial temperature of chocolate = 15C specific heat capacity of chocolate = 3.910³ J kg^–1K^–1 specific latent heat of chocolate = 1.5010⁵J kg^–1 1 kcal = 4200 J

Aluminium is one of the most widely recycled metals. Aluminium cans are heated from room temperature until all the aluminium has melted. The molten aluminium is then used to make new cans. This process uses only 5% of the energy needed to extract aluminium from raw materials.

On a website it is claimed that recycling one aluminium can of mass 14 g saves enough energy to listen to music on a mobile phone continuously for 7 days.

Assess the validity of this claim.

melting point of aluminium = 660 K specific heat capacity of aluminium = 902 J kg⁻¹K⁻¹ specific latent heat of aluminium = 396 kJ kg⁻¹ room temperature = 293 K mobile phone p.d. = 3.7 V mobile phone current = 120 mA

It was suggested on an online forum that it would be possible to cook a chicken by repeatedly slapping the chicken with one hand.

It was claimed that the energy transferred to a chicken in 8000 slaps would be sufficient to raise the temperature of the chicken from 23 °C to 165 °C.

In an investigation to test the claim, the effective mass of the hand was taken as 1.75 kg and the speed of the hand just before impact with the chicken as 6.25 m s⁻¹.

Deduce whether the data confirms that 8000 slaps would be sufficient. Assume that no energy is transferred from the chicken to the surroundings.

mass of chicken = 0.875 kg specific heat capacity of chicken = 1770 J kg⁻¹K⁻¹ efficiency of energy transfer from the hand = 65%

Explain whether the assumption made in (a) is realistic.

Latte is a type of coffee made with hot frothy milk. The milk is heated by pumping steam into it.

Calculate the maximum mass of milk that could be warmed to a temperature of 65 °C by absorbing 15 g of steam at 100 °C.

initial temperature of milk = 4.0 °C specific heat capacity of milk = 3900 J kg⁻¹K⁻¹ specific heat capacity of water = 4200 J kg⁻¹K⁻¹ specific latent heat of vaporisation of water = 2.3 10⁶J kg⁻¹

The apparatus shown can be used to determine a value for the specific latent heat of vaporisation of water.

In one experiment the current in the heater was 8.20 A, and the potential difference across the heater was 230 V.

Show that the power of the heater was about 2 kW.

There was 0.655 kg of water in the flask at an initial temperature of 22.5 °C. The heater was switched on, and the water in the flask was heated to boiling point.

Calculate the minimum time taken for the water to be heated to 100.0 °C.

specific heat capacity of water = 4190 J kg⁻¹K⁻¹

The heater was left on and water continued to boil in the flask. The water was allowed to boil for a few minutes. The conical flask was then placed under the heat exchanger and water was collected in it.

Give a reason why the water was left boiling for a few minutes before the conical flask was put in place.

Water with a mass of 95.0 g was collected in a time of 125 s.

Calculate the rate of energy transfer in the heat exchanger.

specific latent heat of vaporisation of water = 2.26 × 10⁶J kg⁻¹

Discuss your answers to (a)(i) and (b)(ii).

State how the apparatus could be modified to minimise the effect of a significant source of error.

A cup contains 180 g of black coffee at a temperature of 82 °C. 68 g of milk at a temperature of 2.7 °C is added to the coffee. An ideal temperature range for drinking coffee is said to be 50 °C to 60 °C.

Deduce whether the coffee will be within the ideal temperature range when the milk is added.

initial temperature of milk = 2.7 °C

specific heat capacity of black coffee = 4.2 × 10³J kg⁻¹K⁻¹

specific heat capacity of milk = 3.9 10³J kg⁻¹K⁻¹

A cup contains 180 g of black coffee at a temperature of 82 °C. 68 g of milk at a temperature of 2.7 °C is added to the coffee. An ideal temperature range for drinking coffee is said to be 50 °C to 60 °C.

Deduce whether the coffee will be within the ideal temperature range when the milk is added.

initial temperature of milk = 2.7 °C

specific heat capacity of black coffee = 4.2 × 10³J kg⁻¹K⁻¹

specific heat capacity of milk = 3.9 10³J kg⁻¹K⁻¹

A student determined the specific heat capacity of aluminium.

She used an electrical heater to heat an aluminium block and measured the temperature of the block with a digital thermometer.

She connected the electrical heater into a circuit and took measurements to determine the power of the heater.

Draw a circuit diagram of a suitable circuit.

The student monitored the temperature θ of the aluminium block over the time t for which the heater was switched on.

Her results are plotted on the graph.

Determine the specific heat capacity of aluminium.

power of heater = 37.5 W mass of aluminium block = 0.986 kg

The student looked up the accepted value for the specific heat capacity of aluminium. Using this value, the student predicted that it should have taken 240 s for the temperature of the aluminium block to increase by 10 °C.

Explain the difference between the predicted time and the student’s actual observations.

A student carried out an experiment to determine the specific latent heat of vaporisation of water using the apparatus shown.

glass tubing

The water in the flask was heated and steam was forced out of the flask and through the glass tubing into the cold water in the insulated cup. The steam condensed as it passed into the cold water.

The initial temperature of the cold water was 18.5°C and the mass of water in the cup was 255.0 g. After steam had been passed through the water for some time the temperature had risen to 26.0 °C and the mass of the water in the cup was 258.3 g.

Calculate the specific latent heat of vaporisation of water.

specific heat capacity of water = 4190 J kg^–1 K^–1

Explain why the water was heated to boiling point and left boiling for a few minutes before the insulated cup of cold water was put in place.

Identify a significant source of error in this experiment and the steps that should be taken to minimise its effect on the calculated value of the specific latent heat of vaporisation of water.

An electric iron rated at 2600 W contains a steel plate which is heated to a working temperature of 215C. Room temperature is 18C.

Deduce whether the plate could reach its working temperature in less than 1 minute.

mass of steel plate = 890 g

specific heat capacity of steel = 450 J kg^–1K^–1