Would it be more efficient to warm your bed on a cold night with a hot water bottle that contains 1kg of water at 50c with a 1kg gold bar at 50c? Why?
Which has more stored heat? Ans: the one with the highest heat capacity.
dont understand the answer, the question does not say which one has the most stored heat, just the amount of each and temp of each
The answer still is the same. Calcualte the heat stored in the 1 kg water and 1 kg gold and you will know which can produce the most heat to the bed.
q = mass x specific heat x T
To determine which method would be more efficient in warming a bed on a cold night, we need to compare the heat capacities of the hot water bottle and the gold bar.
Heat capacity is the amount of heat required to raise the temperature of a substance by 1 degree Celsius. Different substances have different heat capacities.
The specific heat capacity of water is approximately 4.18 J/g°C, which means it takes 4.18 joules of energy to raise the temperature of 1 gram of water by 1 degree Celsius.
The specific heat capacity of gold is approximately 0.13 J/g°C, which means it takes 0.13 joules of energy to raise the temperature of 1 gram of gold by 1 degree Celsius.
Now, let's calculate the total heat capacity for both the hot water bottle and the gold bar:
For the hot water bottle:
- Mass of water = 1 kg (or 1000 grams)
- Specific heat capacity of water = 4.18 J/g°C
- Temperature change = (50°C - room temperature)
For the gold bar:
- Mass of gold = 1 kg (or 1000 grams)
- Specific heat capacity of gold = 0.13 J/g°C
- Temperature change = (50°C - room temperature)
So, in terms of heat capacity, the hot water bottle would have a much higher capacity to store and transfer heat compared to the gold bar.
Therefore, it would be more efficient to warm your bed on a cold night with a hot water bottle that contains 1 kg of water at 50°C rather than a 1 kg gold bar at 50°C. The water in the hot water bottle can hold more heat energy due to its higher specific heat capacity, resulting in a more effective warming method.