Question

A 1.0 g sample of a cashew was burned in a calorimeter containing 1000. g of water, and the temperature of the water changed from 20.0°C to 25.0°C. In another experiment, a 3.0 g sample of a marshmallow was burned in a calorimeter containing 2000. g of water, and the temperature of the water changed from 25.0°C to 30.0°C. Based on the data, which of the following can be concluded about the energy content for 1.0 g of each of the two substances? (The specific heat of water is 4.2 J/(g⋅°C).) (A) The combustion of 1.0 g of cashew releases less energy than the combustion of 1.0 g of marshmallow. (B) The combustion of 1.0 g of cashew releases the same amount of energy as the^combustion of 1.0 g of marshmallow. (C) The combustion of 1.0 g of cashew releases more energy than the combustion of 1.0g of marshmallow. (D) No comparison can be made because the two systems started with different masses of food, different masses of water, and different initial temperatures.

Answer 1

Answer:

The correct answer is option C.

Explanation:

1.0 g sample of a cashew :

Heat released on  combustion of 1.0 gram of cashew = -Q

We have mass of water = m = 1000 g

Specific heat of water = c = 4.184 J/g°C

ΔT = 30°C - 25°C = 5°C

Heat absorbed by the water :  Q

$Q=1000 g\times 4.184 J/g^oC\times 5^oC=20,920 J$

Heat released on  combustion of 1.0 gram of cashew is -20,920 J.

3.0 g sample of a marshmallows  :

Heat released on  combustion of 3.0 g sample of a marshmallows = -Q'

We have mass of water = m = 2000 g

Specific heat of water = c = 4.184 J/g°C

ΔT = 30°C - 25°C = 5°C

Heat absorbed by the water :  Q'

$Q'=2000 g\times 4.184 J/g^oC\times 5^oC=41,840 J$

Heat released on 3.0 g sample of a marshmallows= -Q' = -41,840 J

Heat released on 1.0 g sample of a marshmallows : q

$q =\frac{-Q'}{3} = \frac{-41,840 J}{3}=-13,946.67 J$

Heat released on  combustion of 1.0 gram of marshmallows -13,946.67 J.

-20,920 J. > -13,946.67 J

The combustion of 1.0 g of cashew releases more energy than the combustion of 1.0 g of marshmallow.

Answer 2

From the calculations, what can be concluded about the energy content for 1.0 grams of each of the two substances (cashew and marshmallow) is: (C) The combustion of 1.0 g of cashew releases more energy than the combustion of 1.0g of marshmallow.

Given the following data:

• Initial temperature of water = 20.0°C

• Final temperature of water = 25.0°C

• Mass of cashew = 1.0 grams

• Mass of water = 1000.0 grams

• Mass of marshmallow = 3.0 grams

• Mass of water = 2000.0 grams

• Specific heat capacity of water = 4.2 J/g°C

• Initial temperature of water 2 = 25.0°C

• Final temperature of water 2 = 30.0°C

To find the energy content of the two substances (cashew and marshmallow):

For cashew:

Mathematically, quantity of heat is given by the formula;

$Q = mc\theta$

Where:

• Q represents the quantity of heat.

• m represents the mass of an object.

• c represents the specific heat capacity.

• ∅ represents the change in temperature.

Substituting into the formula, we have:

$Q = 1000(4.2)(25 - 20)\\\\Q = 4200(5)$

Quantity of heat, Q = 21,000 Joules

For 3.0 g of marshmallow:

$Q = 2000(4.2)(30 - 25)\\\\Q = 8400(5)$

Quantity of heat, Q = 42,000 Joules

By using 1.0 g sample of a marshmallow:

$Q = \frac{42000}{3}$

Q = 14000 Joules.

Based on the above data, the combustion of 1.0 g of cashew releases more energy than the combustion of 1.0g of marshmallow.

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