the specific heat for iron is .450 J/g*K . a piece of iron increases from 27.2C to 31.4 C when of energy is added to it. what is the mass of the iron?

a. 343 g
b. .0029 g
c. 286 g
d. 1.65 * 10^-4 g

2 answers

To find the mass of the iron, we can use the formula for heat transfer:

\[ q = mc\Delta T \]

where:

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

From the problem:

  • The specific heat capacity of iron, \( c = 0.450 , \text{J/g·K} \).
  • Initial temperature, \( T_i = 27.2 , \text{°C} \) and final temperature, \( T_f = 31.4 , \text{°C} \).
  • The change in temperature, \( \Delta T \), is:

\[ \Delta T = T_f - T_i = 31.4 , \text{°C} - 27.2 , \text{°C} = 4.2 , \text{°C} \]

Now, substituting the values into the formula, we can express it in terms of mass:

\[ q = m \cdot 0.450 \cdot 4.2 \] \[ q = m \cdot 1.89 \]

Now we notice that there is no specific value for \( q \) provided in the problem. Therefore, without knowing the heat energy \( q \) that was added, we cannot calculate the mass \( m \) of the iron based on the given options.

If we assume different values for \( q \) to check the options, it won’t yield the correct answer without \( q \). If you have the value for \( q \), please provide that, and I'll help you calculate the mass!

the answer is required pls choose from the asnwer choices
a. 343 g
b. .0029 g
c. 286 g
d. 1.65 * 10^-4 g