A substance has a specific heat of 0.870 J/g°C. It requires 2,000.0 joules to increase the temperature of 10.0 grams of the substance from its original temperature to its final temperature.

By how many degrees did the substance increase?

87.0°C
174°C
230°C
1,740°C

1 answer

To determine the increase in temperature (\( \Delta T \)) of the substance, we can use the formula for heat transfer:

\[ q = m \cdot c \cdot \Delta T \]

where:

  • \( q \) is the heat added (in joules),
  • \( m \) is the mass of the substance (in grams),
  • \( c \) is the specific heat capacity (in J/g°C),
  • \( \Delta T \) is the change in temperature (in °C).

From the problem, we have:

  • \( q = 2000.0 , \text{J} \)
  • \( m = 10.0 , \text{g} \)
  • \( c = 0.870 , \text{J/g°C} \)

We can rearrange the equation to solve for \( \Delta T \):

\[ \Delta T = \frac{q}{m \cdot c} \]

Now, substituting in the values:

\[ \Delta T = \frac{2000.0 , \text{J}}{10.0 , \text{g} \cdot 0.870 , \text{J/g°C}} \]

Calculating the denominator:

\[ 10.0 , \text{g} \cdot 0.870 , \text{J/g°C} = 8.7 , \text{J/°C} \]

Now substituting back into the equation:

\[ \Delta T = \frac{2000.0 , \text{J}}{8.7 , \text{J/°C}} \approx 229.89 , \text{°C} \]

Rounding to one decimal place, we have:

\[ \Delta T \approx 230.0 , \text{°C} \]

Thus, the increase in temperature is approximately \( 230°C \).

The correct answer is 230°C.