The unit energy for melting and pouring for a certain casting metal , its density , and the volume of the casting including riser
and gating system. The total heat required to raise the temperature of the metal to the pouring temperature is closest to which one of the following:
(a) 1000 kJ ,
(b) 2000 kJ ,
© 3000 k ,
(d) 4000 kJ ,
(e) 5000 kJ .
a
c

Ask by Norris Morgan. in the United States

Mar 25,2025

Question

The unit energy for melting and pouring for a certain casting metal , its density , and the volume of the casting including riser
and gating system. The total heat required to raise the temperature of the metal to the pouring temperature is closest to which one of the following:
(a) 1000 kJ ,
(b) 2000 kJ ,
© 3000 k ,
(d) 4000 kJ ,
(e) 5000 kJ .
a
c

Ask by Norris Morgan. in the United States

Mar 25,2025

UpStudy AI · Accepted Answer

To find the total heat required to raise the temperature of the metal to the pouring temperature, we can use the following steps:

1. **Calculate the mass of the casting metal** using the formula:
   $$
   m = \text{density} \times \text{volume}
   $$

2. **Calculate the total heat required** using the formula:
   $$
   Q = m \times \text{unit energy}
   $$

Now, let's perform the calculations step by step.

### Step 1: Calculate the mass of the casting metal
Given:
- Density $$ = 5.0 \, \text{g/cm}^3 $$
- Volume $$ = 600 \, \text{cm}^3 $$

The mass $$ m $$ can be calculated as:
$$
m = 5.0 \, \text{g/cm}^3 \times 600 \, \text{cm}^3
$$

### Step 2: Calculate the total heat required
Given:
- Unit energy $$ = 1000 \, \text{J/g} $$

The total heat $$ Q $$ can be calculated as:
$$
Q = m \times 1000 \, \text{J/g}
$$

Now, let's compute these values.
Calculate the value by following steps:
- step0: Calculate:
  $$5\times 600$$
- step1: Multiply the numbers:
  $$3000$$
Calculate or simplify the expression $$ m * 1000 $$.
Simplify the expression by following steps:
- step0: Solution:
  $$m\times 1000$$
- step1: Reorder the terms:
  $$1000m$$
Calculate or simplify the expression $$ 3000 * 1000 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$3000\times 1000$$
- step1: Multiply the numbers:
  $$3000000$$
### Step 1: Calculate the mass of the casting metal
The mass $$ m $$ is calculated as:
$$
m = 5.0 \, \text{g/cm}^3 \times 600 \, \text{cm}^3 = 3000 \, \text{g}
$$

### Step 2: Calculate the total heat required
Now, substituting the mass into the heat equation:
$$
Q = 3000 \, \text{g} \times 1000 \, \text{J/g} = 3000000 \, \text{J}
$$

To convert this to kilojoules:
$$
Q = \frac{3000000 \, \text{J}}{1000} = 3000 \, \text{kJ}
$$

Thus, the total heat required to raise the temperature of the metal to the pouring temperature is closest to **3000 kJ**.

The correct answer is (c) 3000 kJ.
The total heat required is closest to 3000 kJ.

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Solución

Step 1: Calculate the mass of the casting metal

Step 2: Calculate the total heat required

Step 1: Calculate the mass of the casting metal

Step 2: Calculate the total heat required

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