Would it be more efficient to warm your bed on a cold night with a hot water bottle that contains 1 kg of water at 50 degrees C or with a 1 kg gold bar at 50 degrees C?

To determine which option would be more efficient in warming your bed on a cold night, we need to consider the specific heat capacity of water and gold.

The specific heat capacity is the amount of heat energy required to raise the temperature of a substance by 1 degree Celsius per unit mass.

The specific heat capacity of water is approximately 4.18 Joules per gram per degree Celsius (J/g°C), while the specific heat capacity of gold is about 0.13 J/g°C.

Given that the mass of both the 1 kg water and 1 kg gold bar are the same, we can calculate the total amount of heat energy they contain at 50°C.

For the water:
Q = m * c * ΔT
Q = 1000 g * 4.18 J/g°C * (50°C - 0°C)
Q = 209,000 J

For the gold:
Q = m * c * ΔT
Q = 1000 g * 0.13 J/g°C * (50°C - 0°C)
Q = 6,500 J

Comparing the heat energies of the water and gold, the water-filled hot water bottle contains significantly more heat energy than the gold bar:

Water: 209,000 J
Gold: 6,500 J

Therefore, the hot water bottle with 1 kg of water at 50 degrees C would be more efficient in warming your bed on a cold night compared to the 1 kg gold bar at the same temperature.

To determine which option would be more efficient in warming your bed on a cold night, we need to consider a few factors. The efficiency of warming depends on the ability of the material to retain and transfer heat.

Specific Heat Capacity: The specific heat capacity of a substance is the amount of heat energy required to raise the temperature of a given amount of that substance by 1 degree Celsius. Water has a very high specific heat capacity, approximately 4,186 J/kg·°C, which means it can absorb and store a large amount of heat energy. Gold, on the other hand, has a significantly lower specific heat capacity of approximately 130 J/kg·°C.

Heat Transfer: Another important factor is the ability of the material to transfer heat. Water is an excellent conductor of heat, meaning it can transfer heat efficiently. Gold, while a good conductor of electricity, is not as efficient in transferring heat as water.

Considering these factors, in this scenario, it would be more efficient to warm your bed with the hot water bottle that contains 1 kg of water at 50 degrees Celsius. Water has a higher specific heat capacity and can absorb and store more heat energy, allowing it to keep your bed warm for a longer period of time. Additionally, water can transfer heat more effectively, making it a better choice for this purpose compared to gold.

To wrap it up, the hot water bottle with 1 kg of water at 50 degrees Celsius would be more efficient for warming your bed on a cold night due to its higher specific heat capacity and better heat transfer properties compared to a gold bar.

It would be more efficient with the hot water bottle. The specific heat of water is a whopping 4.2 kJ/kg*°C while that of gold is only 0.13 kJ/kg*°C.

But I still have my bed warmer from Holland hanging on my wall! It's a lovely copper "pot" that held hot coals with a long wooden handle!

Sra (aka Mme)