Mavzu: тermodinamika 1-qonuni termodinamikaning birinchi qonuni nima?

2-masala: geliyni qizdirish
Toʻrtta bir xil idishda teng miqdorda bir xil temperaturadagi geliy gazi bor. Gazlar germetik yopiq qoʻzgʻaluvchan porshen ostiga joylashtirilgan. Har bir gaz quyida keltirilgan turlicha jarayonlarda ishtirok etdi.
1-gaz: 500 \text{ J}500 J500, start text, space, J, end text issiqlik miqdori gazdan chiqib ketdi va gaz 300 \text{ J}300 J300, start text, space, J, end text ish bajardi
2-gaz: 500 \text{ J}500 J500, start text, space, J, end text issiqlik miqdori gazga berildi va gaz 300 \text{ J}300 J300, start text, space, J, end text ish bajardi
3-gaz: 500 \text{ J}500 J500, start text, space, J, end text issiqlik miqdori gazdan chiqib ketdi va gaz ustida 300 \text{ J}300 J300, start text, space, J, end text ish bajarildi
4-gaz: 500 \text{ J}500 J500, start text, space, J, end text issiqlik miqdori gazga berildi va gaz ustida 300 \text{ J}300 J300, start text, space, J, end text ish bajarildi
Gazlar ushbu jarayondan oʻtgandan keyin ularning temperaturalari orasidagi munosabat qanday boʻladi?
A. T_4>T_3>T_2>T_1T4​>T3​>T2​>T1​T, start subscript, 4, end subscript, is greater than, T, start subscript, 3, end subscript, is greater than, T, start subscript, 2, end subscript, is greater than, T, start subscript, 1, end subscript
B. T_1>T_3>T_2>T_4T1​>T3​>T2​>T4​T, start subscript, 1, end subscript, is greater than, T, start subscript, 3, end subscript, is greater than, T, start subscript, 2, end subscript, is greater than, T, start subscript, 4, end subscript
C. T_4>T_2>T_3>T_1T4​>T2​>T3​>T1​T, start subscript, 4, end subscript, is greater than, T, start subscript, 2, end subscript, is greater than, T, start subscript, 3, end subscript, is greater than, T, start subscript, 1, end subscript
D. T_1>T_4>T_3>T_2T1​>T4​>T3​>T2​T, start subscript, 1, end subscript, is greater than, T, start subscript, 4, end subscript, is greater than, T, start subscript, 3, end subscript, is greater than, T, start subscript, 2, end subscript
Yechish:
ichki energiyasi \Delta UΔUdelta, U eng koʻp ortgan gazning temperaturasi \Delta TΔTdelta, T eng yuqori boʻladi (chunki temperatura va ichki energiya oʻzaro proporsional). Ichki energiya qanday oʻzgarganini topish uchun biz termodinamikaning birinchi qonunidan foydalanamiz.
1-gaz:
\begin{aligned} \Delta U&=Q+W \\ \Delta U&=(-500\text{ J})+(-300\text{ J}) \\ \Delta U&=-800\text{ J} \end{aligned}ΔUΔUΔU​=Q+W=(−500 J)+(−300 J)=−800 J​
2-gaz:
\begin{aligned} \Delta U&=Q+W \\ \Delta U&=(+500\text{ J})+(-300\text{ J}) \\ \Delta U&=+200\text{ J} \end{aligned}ΔUΔUΔU​=Q+W=(+500 J)+(−300 J)=+200 J​
3-gaz:
\begin{aligned} \Delta U&=Q+W \\ \Delta U&=(-500\text{ J})+(300\text{ J}) \\ \Delta U&=-200\text{ J} \end{aligned}ΔUΔUΔU​=Q+W=(−500 J)+(300 J)=−200 J​
4-gaz:
\begin{aligned} \Delta U&=Q+W \\ \Delta U&=(+500\text{ J})+(+300\text{ J}) \\ \Delta U&=+800\text{ J} \end{aligned}ΔUΔUΔU​=Q+W=(+500 J)+(+300 J)=+800 J​
Temperaturalar orasidagi bogʻlanish xuddi ichki energiya oʻzgarishiniki bilan bir xil boʻladi (yaʼni 4-gazning ichki energiyasi eng koʻp ortgan, demak, 4-gaz eng katta temperaturaga erishgan).
\Delta U_4>\Delta U_2>\Delta U_3>\Delta U_1ΔU4​>ΔU2​>ΔU3​>ΔU1​delta, U, start subscript, 4, end subscript, is greater than, delta, U, start subscript, 2, end subscript, is greater than, delta, U, start subscript, 3, end subscript, is greater than, delta, U, start subscript, 1, end subscript va T_4>T_2>T_3>T_1T4​>T2​>T3​>T1​