Some very hot rocks have a temperature of #420 ^o C# and a specific heat of #250 J/(Kg*K)#. The rocks are bathed in #35 L# of boiling water. If the heat of the rocks completely vaporizes the water, what is the minimum combined mass of the rocks?

Answer 1

The mass of the rocks is #=987.4kg#

The heat transferred from the hot rocks to the water, is equal to the heat used to evaporate the water.

For the rocks #DeltaT_o=420-100=320^@C#

Heat of vaporisation of water

#H_w=2257kJkg^-1#

The specific heat of the rocks is

#C_o=0,25kJkg^-1K^-1#
The mass of water is #m_w=35kg#
# m_o C_o (DeltaT_o) = m_w H_w #
#m_o*0.25*320=35*2257#

The mass of the rocks is

#m_o=(35*2257)/(0,25*320)#
#=987.4kg#
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Answer 2

The heat required to vaporize the water can be calculated using the formula: ( Q = m \cdot c \cdot \Delta T ), where ( Q ) is the heat, ( m ) is the mass, ( c ) is the specific heat, and ( \Delta T ) is the change in temperature. Given that the water is boiling at 100°C and starting at room temperature, the change in temperature is ( \Delta T = 100 )°C. Substituting the given values, we can solve for the mass of the water. Then, knowing that the heat absorbed by the water equals the heat released by the rocks, we can calculate the combined mass of the rocks and water.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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