When a piece of copper weighing 250 grams is placed n a cup with 450ml of H2O at 21C and the Cp of te cupis 47J/K, how many grams of gasolne would it tae to heat the system to 110C?

To solve this problem, we need to calculate the amount of energy required to heat the system from 21°C to 110°C and then determine how many grams of gasoline would provide this amount of energy.

To calculate the energy required to heat the system, we can use the formula:

Q = mcΔT

Where:
Q is the energy required (in Joules)
m is the mass of the copper (in grams)
c is the specific heat capacity of water (in J/g°C)
ΔT is the change in temperature (in °C)

Let's first calculate the energy required to heat the water in the cup:

m_water = 450 ml
The density of water is approximately 1 g/ml, so
m_water = 450 g

c_water = 4.18 J/g°C (Specific heat capacity of water)

ΔT_water = (110°C - 21°C) = 89°C

Q_water = m_water * c_water * ΔT_water

Now, let's calculate the energy required to heat the copper:

m_copper = 250 g (Mass of copper)

c_copper = 0.385 J/g°C (Specific heat capacity of copper)

ΔT_copper = (110°C - 21°C) = 89°C

Q_copper = m_copper * c_copper * ΔT_copper

To find the total energy required to heat the system, we sum the energies for water and copper:

Q_total = Q_water + Q_copper

Now, we need to determine the amount of gasoline required to provide this energy.

The energy content of gasoline is typically measured in units of energy per mass. For this calculation, we'll use the energy content of gasoline as approximately 35 Megajoules per kilogram (MJ/kg).

First, we need to convert the total energy required (Q_total) from Joules to Megajoules:

Q_total_MJ = Q_total / 10^6

Next, we calculate the mass of gasoline required:

Mass_gasoline = Q_total_MJ / 35

Finally, we have the mass of gasoline required to heat the system from 21°C to 110°C.

Please note that these calculations are approximations, and actual values may vary slightly due to factors such as latent heat and variations in specific heat capacities.