Determination of the specific heat of the test object material considering the heat capacity of the calorimeter cup

Determine the specific heat of the substance using the calorimetric method, taking into account the heat capacity of the inner cup of the calorimeter.

We derive the final formula for the experiment

Kui katsekeha jahtub, saab selle käigus eralduva soojushulga arvutada nii:

Q_{1} = c_{k} m_{k} (t_{k2}^{\circ} - t_{k1}^{\circ})

Kui vesi saab katsekeha jahtumisel soojust juurde, saab selle juurdesaadava soojushulga arvutada niimoodi:

Q_{2} = c_{v} m_{v} (t_{v2}^{\circ} - t_{v1}^{\circ})

Lisaks neile on meil nüüd ka kalorimeetri tops:

Q_{3} = c_{Al} m_{t} (t_{t2}^{\circ} - t_{t1}^{\circ})

Katse lõpus on vee, katsekeha ja topsi temperatuurid võrdsustunud, seega:

t_{k2}^{\circ} = t_{v2}^{\circ} = t_{t2}^{\circ}

Energia jäävuse seadus ütleb, et katsekehast eralduv ja veele ning topsile juurde antav soojushulk peavad võrduma:

- Q_{1} = Q_{2} + Q_{3}

Asendame avaldised $Q_{1}$ , $Q_{2}$ ja $Q_{3}$ jaoks

- c_{k} m_{k} (t_{k2}^{\circ} - t_{k1}^{\circ}) = c_{v} m_{v} (t_{v2}^{\circ} - t_{v1}^{\circ}) + c_{Al} m_{t} (t_{t2}^{\circ} - t_{t1}^{\circ})

Et $t_{k 2}^{\circ} = t_{v 2}^{\circ} = t_{t 2}^{\circ}$ , võime mõlemad temperatuurid ühesuguse tähistuse alla tuua, näiteks $t^{\circ}$ . Nii saame

- c_{k} m_{k} (t^{\circ} - t_{k1}^{\circ}) = c_{v} m_{v} (t^{\circ} - t_{v}^{\circ}) + c_{Al} m_{t} (t^{\circ} - t_{t1}^{\circ})

Teisendades saame katsekeha materjali erisoojuse valemiks

c_{k} = - \frac{c_{v} m_{v} (t^{\circ} - t_{v}^{\circ}) + c_{Al} m_{t} (t^{\circ} - t_{t1}^{\circ})}{m_{k} (t^{\circ} - t_{k1}^{\circ})}

Ilma kalorimeetri topsi soojusmahtuvust arvestamata oleks valem selline

c_{k} = - \frac{c_{v} m_{v} (t^{\circ} - t_{v1}^{\circ})}{m_{k} (t^{\circ} - t_{k1}^{\circ})}

How we calculate

Niisiis, tundmatust materjalist katsekeha erisoojuse arvutamiseks, arvestades kalorimeetri sisemise topsi soojusmahtuvust, on meil vaja

Vee massi - $m_{v}$
Keha massi - $m_{k}$
Topsi massi - $m_{t}$
Vee algtemperatuuri - $t_{v1}^{\circ}$
Vee lõpptemperatuuri - $t_{v2}^{\circ}$
Keha algtemperatuuri - $t_{k1}^{\circ}$
Keha lõpptemperatuuri - $t_{k2}^{\circ}$
Topsi algtemperatuuri - $t_{t1}^{\circ}$
Topsi lõpptemperatuuri - $t_{t2}^{\circ}$
Vee erisoojust - $c_{v}$
Alumiiniumi erisoojust - $c_{Al}$

Arvutamiseks kasutame valemit

c_{k} = - \frac{c_{v} m_{v} (t^{\circ} - t_{v}^{\circ}) + c_{Al} m_{t} (t^{\circ} - t_{t1}^{\circ})}{m_{k} (t^{\circ} - t_{k1}^{\circ})}

How to conduct the experiment: instructions

Weigh the mass of the test object.
Weigh the cup of the calorimeter, pour about $100 m l$ of cold water into the cup, weigh the total mass of the cup and water.
Place one temperature sensor in the calorimeter, the other in the hot water.
Drop the test object tied to the end of the thread into the hot water and wait until thermal equilibrium occurs.
Record the temperatures of the water in the calorimeter and the hot water heating the test body.
Remove the test piece from the hot water and place it in the cold water in the calorimeter cup.
Stir the water until the temperature in the calorimeter stops changing.
Record the temperature of the water in the calorimeter.
Calculate the specific heat of the substance of the test object.

How to conduct an experiment

Test data

Test object mass $m_{k}$ ( $k g$ )
Mass ( $k g$ ) of the aluminum calorimeter cup
Total mass of cold water and calorimeter cup ( $k g$ )
Mass of cold water $m_{v}$ ( $k g$ )
Specific heat of water ( $\frac{J}{k g \cdot^{\circ} C}$ )
Specific heat of aluminum ( $\frac{J}{k g \cdot^{\circ} C}$ )
Initial temperature of cold water $t_{v 1}^{\circ}$ ( $^{\circ} C$ )
Initial temperature of the test object (hot water temperature) $t_{k 1}$ ( $^{\circ} C$ )
The final temperature of the cold water and the test object $t^{\circ}$ ( $^{\circ} C$ )

Results

Specific heat without considering the heat capacity of the calorimeter cup ( $\frac{J}{k g \cdot^{\circ} C}$ )
Specific heat considering the heat capacity of the calorimeter cup ( $\frac{J}{k g \cdot^{\circ} C}$ )

The table shows the specific heats of several well-known substances.

Comment

All sources of error mentioned in the question are real, although they affect the result to varying degrees.

The bottommost, unexplained row of the results table gives the automatically calculated value based on the test results.