Specific heat capacity Quiz 1

Question 1

You decide to bake some brownies for which you need melted butter at room temperature which is at around $$27^{\circ}C$$, as the recipe recommends. You stick $$100\,g$$ of butter in the microwave oven but you forget to keep an eye on it. The butter begins to boil upon reaching a $$110^{\circ}C$$ and you immediately remove it and place it in a water bath containing $$250\,ml$$ of water at room temperature until the butter cools to the recommended temperature. Find the specific heat capacity of the butter if the final temperature of the water is found to be $$43.5^{\circ}C.$$ $$(	ext{Take density of water as}\,ho = 1\,gcm^{-3}\ 	ext{and specific heat capacity of water}\,s_{w} = 4182\,J\,kg^{-1}K^{-1})$$

Accepted Answer

$$2.08\,kJ\,kg^{-1}K^{-1}$$

Answer

$$4.18\,kJ\,kg^{-1}K^{-1}$$

Answer

$$3.77\,kJ\,kg^{-1}K^{-1}$$

Answer

$$5.69\,kJ\,kg^{-1}K^{-1}$$

Question 2

The $$10^{15}\,W$$ or the 10-petawatt laser developed at the Nuclear Physics facility of the European Light Infrastructure (ELI) project is a massive and the most powerful laser ever developed whose power output corresponds to more than $$10\%$$ of the power that the Earth receives from the Sun. If it pulses out a $$230\,J$$ beam that is incident on a $$750\,g$$ cube of gold that gets heated from $$25^{\circ}C$$ to $$27.38^{\circ}C$$ instantly, find the specific heat capacity of the gold.

Accepted Answer

$$0.129\,Jg^{-1} {}^{\circ}C^{-1}$$

Answer

$$0.234\,Jg^{-1} {}^{\circ}C^{-1}$$

Answer

$$0.601\,Jg^{-1} {}^{\circ}C^{-1}$$

Answer

$$0.923\,Jg^{-1} {}^{\circ}C^{-1}$$

Question 3

One of the benefits of copper that is backed by science is its antibacterial effect. Contaminated water can contain considerable amounts of bacteria that can cause digestive disorders. Storing water in a copper pot causes extensive damage to the cell walls of the bacteria when they come in contact with the mineral walls of the pot leading to their death. Imagine you obtain water from a hot spring. The water cools down from $$75^{\circ}C$$ to $$25^{\circ}C$$ by losing $$50 	imes 10^4\,J$$ of its thermal energy to the walls of the vessel. If the specific heat capacity of water is $$4.2 	imes 10^{3}\,Jkg^{-1}\,^{\circ}C^{-1}$$, determine the volume of water stored in the vessel. $$(	ext{Take density of water}\,ho = 997\,kgm^{-3})$$

Accepted Answer

$$2.4\,litres$$

Answer

$$1\,litre$$

Answer

$$4.8\,litres$$

Answer

$$4.2\,litres$$

Question 4

The following figure shows an apparatus that is used to measure the specific heat capacity of a block of solid of mass $$\,m$$ insulated from surroundings. The heating element heats up the solid while the thermometer measures the change in temperature of the solid (\Delta T) in time $$t$$. If the current flowing through the heating element is$$\,I$$ indicated in the ammeter due to a potential difference $$\,V$$ as indicated by the voltmeter, determine the specific heat of the block of solid.<img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/b51caf30-984b-4191-8037-d0cd0cfe08d36629746857880771028.png"/>

Accepted Answer

$$\dfrac{IVt}{m\Delta T}$$

Answer

$$\dfrac{It}{Vm\Delta T}$$

Answer

$$\dfrac{Vt}{\Delta T}$$

Answer

$$\dfrac{IV}{m\Delta T}$$

Question 5

Automotive cooling systems work by passing a liquid coolant through the pipes and passages surrounding the engine block. As the coolant flows through these passages it picks up heat from the engine and makes its way through a hose to the radiator at the front end of a car where the stream of air entering the engine compartment via the grills of the car cools the heated coolant.$$\$$ Having understood how this system works you decide to probe into the thermodynamics of the coolant in your car. You find that there is $$5\,litres $$ of coolant, which is an equal-parts mixture of water and antifreeze $$(	ext{ethylene glycol})$$. It absorbs a heat of $$73.5 	imes 10^3\,J$$, lowering the temperature of the engine compartment from $$105^{\circ}C$$ to $$88^{\circ}C$$ while maintaining a constant pressure. Determine the specific heat capacity of the coolant, if it has a density of $$1055\,kgm^{-3}$$.

Accepted Answer

$$0.82\,Jg^{-1}K^{-1}$$

Answer

$$0.41\,Jg^{-1}K^{-1}$$

Answer

$$410\,Jg^{-1}K^{-1}$$

Answer

$$820\,Jg^{-1}K^{-1}$$